tweedy2271592 wrote an answer about MontBell Breeze Dry-Tec U.L Sleeping Bag Cover on September 20, 2009
You certainly could do that, but I bet it'd be a big pain. (I've never tried it myself.) The cover is waterproof/breathable, so it's going to be difficult to get all of the air out when you're trying to stuff it.
BUT it's super easy to take your bag in and out of the cover, and the cover compresses by itself down quite small, so packing them separately shouldn't be a problem.