I've done it with several bikes as I've gotten older, stiffer and less interested in looking like a racer. I have mustache bars inverted on an old Trek, three-speed-style sweptback bars on my Atlantis and a long stem on my Rambouillet to bring the bars up level with the saddle. It always works, makes me more comfortable and doesn't seem to hurt anything. There's certainly more aero drag, but I don't feel it and don't care anyway.
Only thing to watch for is compatibility. Not all bars fit all stems and not all brake and shift levers fit all bars. But there aren't many sizes, and you can almost always work it out.