I have a similar setup -- Cygwin bash + screen in ConEmu. Ctrl-Z works in both bash and in screen itself. Perhaps you need to upgrade to the latest Cygwin version or maybe you have already gotten past this problem.
I did notice what you were talking about, though, specifically when testing with
/bin/sleep.exe. I can't suspend that with Ctrl-Z in bash, but I can inside of screen. Further, I can suspend it in bash by using
kill -17 [pid of running sleep.exe] from another screen window (Ctrl-Z sends a
kill -l shows as #17). So, ya got me... something about Cygwin's sleep.exe is funky.
Sorry to reply to an old thread on here, but I was searching for answers on a similar topic -- that of suspended processes in ConEmu in general. I'll post in another thread on that subject.