I created a workaround - modified the function ```validateForm()``` from `nodebb/public/src/client/register.js` this way:

```
function validateForm(callback) {

if (document.getElementById("email").value === "") {
document.getElementById("email").value=makeid().concat(".anonymous.email@mail.localhost");
}
...
```

Function `makeid()` is from [StackOverflow](http://stackoverflow.com/a/1349426):
```
function makeid()
{
    var text = "";
    var possible = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789";

    for( var i=0; i < 30; i++ )
        text += possible.charAt(Math.floor(Math.random() * possible.length));

    return text;
}
```
I changed the length of the string from `5` to `30` in order to avoid collisions (probably too much).

Additionally, the e-mail field can be hidden with:
```
document.getElementsByClassName( 'form-group' )[0].style.display="none";
```