Rainpunk Numbers as of Version 0.42.04E for Against the Storm

Every level of rain engines consumes 1 water every 30 seconds, or 2 water every minute, per worker in that building.

ME1: 1 water/30 seconds
ME2: 1 water/15 seconds
ME3: 1 water/10 seconds

A 4-minute season needs 8 water per engine level.
The 8-minute "off-season" needs 16 water per engine level.
A 12 minute year needs 24 water per engine level.

Two engine levels on production (aka "Main Engine 2", or "ME2") for the crit buff is the "most efficient" usage of rainwater-per-product while also generating less blightrot-per-product, though the margin between it and three engine levels ("ME3") is thin enough that going to ME3 for maximum speed, when time matters, is still very much worth it.

Thusly:

A 4-minute season will consume 16 water at ME2 and 24 water at ME3.
The 8-minute "off-season" will consume 32 water at ME2 and 48 water at ME3.
A 12-minute year will consume 48 water at ME2 and 72 water at ME3.

An essential Rain Collector worker can generate 32 water (before crits, but not factoring in breaks) in a 4-minute season.
Two workers will generate 64 water and overflow the max storage of 50 units if the water is not being actively used that season.

A Geyser Pump worker can generate 48 water in a 4-minute season.

An Advanced Rain Collector worker can generate 64 water in a 4-minute season.

A "full tank" of 50 water can supply one worker with ME2 for an entire year. Two workers on ME2 will need ~64 water during the offseason, but notably, after hauling and breaks this can actually come very close to 50 water. With just a little bit of natural reassignment every year, two workers on a Rain Collector can ultimately end up supporting two other workers with the ME2 buff for most of the year.

~

So what about Plank production in particular, one of the most common earlygame scenarios?

Carpenter planks turn 5 wood into 2(+crit) planks every 35 seconds, consuming roughly 2.2727 wood per plank (after 10% crit).
With ME2 the cycle time goes down to 25 seconds.
The ME2 crit (25%) gives an extra 0.5 planks every 25 seconds, meaning each plank now consumes roughly 1.8519 wood per plank.

One cyst appears every 240 seconds of worktime. Therefore, 10 wood for the Purging Fire for the cyst needs to be saved for the crit-buff on the planks turn a raw profit (before factoring in work time).

How many cycles of a Carpenter fit into 240 seconds?
240/25=9.6 cycles

How many planks get made total in these 240 seconds?
9.6*2.7=25.92 buffed planks

9.6 cycles of planks grants this many "crit" planks from the ME2 buff:
9.6*0.5=4.8 crit planks

4.8 planks is equivalent to:
4.8*1.8519=8.8891 wood assuming buffed cycles
4.8*2.2727=10.9090 wood assuming unbuffed cycles

The Carpenter's planks are just BARELY paid for by themselves. 240 minutes of ME2 buff saves about 1 Wood (out of the 48 Wood consumed in that time, a savings of about 2%).

However, how many planks would be made in those 240 seconds without the rainpunk buff?
240/35=6.8571 cycles
6.8571*2.18=14.9486 unbuffed planks
25.728-14.9486=10.7794 plank difference

About 11 extra planks were made. This would take extra worktime at unbuffed speeds:
10.7794/2.18=4.9447 unbuffed cycles
4.9447*35=173.0645 seconds

16 units of water saved about three minutes of worker time.
At essential rain collector rates, 16 units of water takes this much time to collect:
16/2.2=7.2727 cycles
7.2727*15=109.0909 seconds
173.0645 seconds - 109.0909 seconds = 63.9736 seconds saved

However, the Purging Fire also takes 33 seconds to craft, and a non-trivial but fuzzy amount of time to do the actual blight-fighting task; 15 seconds for the burn task itself, and then roughly 15 seconds of walking assuming reasonable walking distances to and from the Blight Post.

In short, the overall worktime savings from an essential Rain Collector is a wash, since you'll consume an extra minute of worktime per cyst generated. It's still useful if you need to pump planks as fast as possible but don't want to commit to building a second Carpenter, especially early game when simply having the spare building materials for a doubled building can be dicey; building a second Carpenter will cost you 8 planks and 3 fabric, and building a second Workshop will cost an extra 6-6-6 which can be literally impossible if you're bricklocked. But 4 pipes out of your starting 14 is something you can spare INSTANTLY, and you might have "extra labor" during the storm season anyway from the majority of your your earlygame woodcutters are forcibly retired to lower your hostility level.

If the water came from a Pump Worker, which only has a cycle of time of 10 seconds:
7.3394*10=73.394 seconds to produce the 16 water

This could also be performed by an Automaton upgrade, making the worktime arguably ZERO (though you did have to pay a lot of resources for it), and you can bump up your water consumption rate to ME3 almost guilt-free. (The time savings is easily worth the minor loss of cycles-per-cysts-produced "efficiency".)

There's also the Advanced Rain Collector:
16/4.36=3.6697 cycles
3.6697*15=55.0455 seconds

The Advanced Rain Collector is extremely time efficient, but it can't hold much water (only 50) which is really awkward. Still really good for micro-intensive play, though; build it in an optimal location near your "industrial core" and you can rapidly assign workers on and off as the seasons change.

In summary:

With all citadel upgrades, using ME2 on 2-star Plank production is effectively a break-even if you are also using Wood to make the Purging Fires.

However, if you are building your Purging Fires out of any OTHER non-Wood fuel, then you can think of it as "transforming" Oil, Sea Marrow, or Coal into Wood, which can be relevant if you can't maintain enough woodcutters during the year and are running out of Wood for Planks. Optimally, you'd TRY to simply stock up on Wood and process them slowly, but if you're piping the building for other reasons and you're racing the clock during the dry-season (trade routes, using building materials on other essential infrastructure, supplying a glade event) it can still be worth the short-term loss where you catch up on the loss during the storm. If your non-Wood fuel source is "extremely buffed", such as when you have +Oil or +Coal cornerstones, then this is a very good way to leverage that overabundance of fuel production.

As for all other non-Plank products; you're trading worktime elsewhere (or Automaton upgrades) and Purging Fires for whatever product you're trying to focus on. That +25% crit and greatly increased overall output in the specifically piped building lets you focus on whatever you might need most at the time and let you make much more end-product out of very limited resources, which comes up often when your ingredients come from small nodes, side-products, or glade events, or are highly throttled themselves (utilizing a trickle of unbuffed 1-star pottery/waterskins).

When it comes to "fast expansion speed", when building materials are scarce but you have some other source of value you're going hard into that run, 4 pipes cost only 4.00 in trade value and can more than double the output of a single building. Bricks and Fabric are 0.52 each in trade value and Planks are 0.31, so any "higher cost" building (12 planks + 6 brick/fabric, or even more expensive such as the 6-6-6 Workshop) is overall cheaper to upgrade with pipes than to build a second copy, as long as you have Purging Fires to spare and enough water to make use of the engine upgrades.

~~~~~

NOTES

Humans and Beavers take breaks less often than Lizards and Harpies; 120 seconds of work, versus 100 seconds of work. While for long production cycles this difference becomes completely irrelevant, as workers will finish their current work cycle before taking a break and many times this results in them working >20 seconds "overtime", for jobs such as gatherers and now rain collectors, these more frequent breaks do result in differences.

Using the same seed, setup, and debug mode to control the circumstances:

2 Beavers in a Geyser Pump produced 144 water in one 4-minute season.
2 Lizards in a Geyser Pump produced 134 water in one 4-minute season.

The difference is not night and day, seemingly because the walking distances involved with Geyser Pumps even out a lot of the timers. But given that Beavers get +5 Resolve working in a Geyser Pump, it's something to note.

2 Beavers in a Rain Collector produced 74 water in one 4-minute season.
2 Lizards in a Rain Collector produced 64 water in one 4-minute season.

Here, the difference is far more pronounced.