--msdb query

    select
        case
            when object_id('dbo.sysdac_instances') is not null then 1
        else
            0
        end

--master query

SELECT
dtb.name AS [Name],
dtb.database_id AS [ID],
CAST(has_dbaccess(dtb.name) AS bit) AS [IsAccessible]
FROM
master.sys.databases AS dtb
ORDER BY
[Name] ASC