Of course. I once had the displeasure of being made to shoot a Beretta 391 Sport ("Just try it out!") that had a barrel weight AND a stock weight added. Go figure... the guy buys a lightweight gun and then proceeds to make it into a heavy gun by adding weight, but of course the weight he added is in the ends.

It wouldn't move. Remember playing with a gyroscope toy? Same feel. Rigidity in space, they call it...

"The price of good shotgunnery is constant practice" - Fred Kimble