The process will need to be processing Windows messages timely, in addition to doing what itís regularly doing, which pretty much calls for a secondary thread to do the work while the primary thread listens for mouse-moves and keystrokes.
Yet more crap!
Any windows process can be suspended and resumed. And when it is resumed, it will carry on from where it left of with no knowledge it was ever suspended.
If it is a gui process, its screen will not respond to input while it is suspended. But a) there is no suggestion in the OP that this is a gui program; b) so what if it is.
By way of demonstration, I suspended my browser after typing that last paragraph and the resumed it a couple of minutes later to type this one. And ``""'**NOTHING BAD HAPPENED!**'""''