Just in case anyone was wondering, yes you DO lose Mr. Handy if you delete a room while they are in there. I just accidently did it and they don't come back if you rebuild that room.

Also, I can't place another Mr. Handy there now.

I've done the same thing and Mr. Handy just moved to the nearest room. Was the entire row empty?

Nevermind. I exited to the main menu and re-entered the vault and he re-appeared. Phew thought I had lost a Mr. Handy.