Does anyone know what this noise could be?

[Frodo]

Drive it 10 min (or whatever) until you hear the noise. Shut the car down for a couple min. Re-start. Is the sound back immediately? If so, you should be able to test it. I don't think having the belt off is a problem until it's been long enough to start overheating (you're disconnecting the water pump). That should take a few minutes I would think.

I've driven around (briefly...it gets incredibly warm when you do this!) with the carpeting and cover plate off. Just make sure there's no loose clothing, etc, that could get caught in the belt/pulley system! You'll get some idea if it's one of the pulleys doing this even before removing the belt. And it'll be easier/quicker to remove the belt.