Any idea how long it takes from reporting a suspect to getting a reply?

I reported one player and chess.com deleted the account the same day. Maybe it depends on how easy it is to prove.

Good point. It's been a week for me and no news at all. I just want to know whether to resign the games and wish the fella luck or enjoy seeing him time out!

Personally I would wait till he times out and watch as you claim the points if he was stupid enough to cheat in the first place 

Of course, he'll only time out if he's locked out for cheating...