I probably don't need to leave them disconnected. I did it in the short term just to try and get it working. The amount of power that the case fan(s) suck is negligible, but they added a layer of complication to the wiring that was making things awkward at the time.

I'm going to hook one of them back up again tonight and see what happens. The CPU and Video card don't seem to be tossing a lot of heat, but you could cook an egg in the flow coming out from the power supply (well, it's not quite THAT hot, but it's pretty warm).