I've seen some Windows programs work after being dragged to another location, but there is the distinct possibility it will break. You could try it to see. If not, figure out where your saved games are located, secure them, then reinstall it to the new location. Depending on where they are, like your documents folder, you might not have to do anything with them and they should still work.
The Registry is one of several reasons I've always disliked Windows...
All Blizzard games are free of this restriction. You can copy them from place to place without having to reinstall. They intentionally design the games to do this. If they can do it, everyone can do it, but most are too lazy to actually code it right.