Yeah, like Mark said, the GUI versions of both Vim and Emacs are as mouse-controllable as any other editor, from moving the cursor, to menus that do a variety of things, to file dialogs, etc. In fact, CLI Vim can be configured to use the mouse to at least move the cursor, if not other things, if it's in an xterm or some other compliant terminals. That probably applies to Emacs as well.

Of course, this raises the question of why you want to use the mouse to do that sort of stuff. It's way easier and faster to not use it.