There's a reason I don't EVER use my travel luggage as range bags. That reason is because I'm way too pretty for prison.
I agree with Gaerek... there's just nothing to be gained by trying to make the bags do double duty. If you get a screener or airport police who want to raise a stink, I expect it won't take too many lawyer hours to cover the cost of a set of quality travel luggage (I know what I paid for our Victorinox Werks 2.0 stuff, and it wasn't cheap, and even then it would probably only scratch the surface of legal fees for a very minor misdemeanor case).
Better to spend the money up front, have separate bags for each purpose, and never worry about a rogue magazine (or worse, pistol) getting found at the worst possible time.