Signal Desktop works without having your phone turned on. It acts like a full, independent client after linking it to your smartphone app (unlike WhatsApp, which does require your phone to be turned on).
So I guess there is a way to use signal without having a phone nowadays! That's a great news!
I will try right now.
Edit: It actually has the option to register without smartphone, but it's only enabled in the debug versions.
Nor would I since it still requires a phone number to use.
This might get you started: https://github.com/WhisperSystems/Signal-Desktop/blob/d1f7f5...