Yes. It uses the phone number as the user identifier, and the non-phone versions assume that you have a phone that you're using as the primary device, and any o

Yes. It uses the phone number as the user identifier, and the non-phone versions assume that you have a phone that you're using as the primary device, and any other devices are secondary. The primary device is mostly because tablets and desktops don't have a phone number to use as an identifier. The battery/connectivity status of that device doesn't matter a whit after the secondary devices are setup.