What bees will do depends on what is happening. If the top super is drawn comb and you prop up the inner cover, or add a imire shim (3/4" shim with a 3/8" high entrance in it.) then they will probably just use it as an entrance and not burr it all up with comb. If the top super is foundation and the bees are busy drawing it, they will just keep drawing and burr it all up and it will be a bit of a mess.
Personally, I cut a couple of extra holes in the inner cover (about the size of the normal one in the middle, but they could be round if it's easier to do with a hole saw on a drill. Often I cut them with a hole saw the size of a quart jar lid so I can feed through them.) and cover the holes with hardware cloth. Either make a vent box from 1 x 6" or use a shallow or medium box and drill holes around the sides and cover these on the inside with hardware cloth. Now put the ventilated inner cover on with the ventilated box on top of that and a lid on top of that. If you want to save on lids, just cut a piece of plywood to fit the top of the vent box.
I have the most luck with this. Also, if you're making your own bottom boards, put the hive with the opening the long ways.
Here's a ventilated inner cover:
http://www.beesource.com/eob/althive/bush/bush6.htm
Here's the ventilated top box:
http://www.beesource.com/eob/althive/bush/bush3.htm