Can confirm it does work with the coin generation in the Hideout Base:
Can also confirm that it does not work with the improvement room - so the time savings on upgrade/digging for new rooms does not get any better by putting that room next to a generator.
I don't have a layout that I can incorporate the experience room with, but given that it's worked with the other rooms that produce things over time, it probably works there too. I just can't confirm that for certain.