If QubesOS supports Flatpaks sufficiently, then it might run the Signal Desktop app (though if you want to register a new account, you do have to have a phone number, which is also possible virtually these days anyway)
Only if you use a phone with it. Does the official server actively filter numbers from VoIP providers?
As much as I want to say "screw the developer's nonsense, just compile it yourself and do as you please" honestly why bend over backwards to use such a platform when solutions such as Matrix are available?