screen (and tmux) start a new instance of the shell, which would have no knowledge of the backgrounded process. You'd just see the message "fg: no current job"
And even if you could(1), the background process typically has the terminal open - and screen uses a separate pseudo terminal aka pty -- As suggested by the name - rePTYr
(1) ^Z sends SIGSTOP; to continue you can signal SIGCONT. But then what?!
