yes, yes, yes.
Amongst one of the benefits/uses of tmux is to allow persistence of sessions even if disconnected from the session - this was true even before mosh came along.
tmux handles the signal when you disconnect and the processes running in the session continue without being aware a disconnect happened (similar to launching the process via nohup).
So why is above going to result in 'yes, yes, yes' ?
(1) re-attach to my local tmux session,
Yes, because if you are disconnected from the local tmux session, tmux will handle the SIGHUP and will be still continue to run and so when you reconnect you can tmux attach-session
(2) still see my mosh connection alive,
Yes, because tmux handled the disconnection signal, the mosh process running within tmux would continue unaware your connection had disconnected and would continue running.
(3) still the server process running and displaying its output in it?
Yes, because mosh still connected and running the server process would still be going and sending output.