I looked into this option, restoring WhatsApp from a backup does not do it, that is just the historic chat data backed up, useful after activating and verifying WhatsApp first.... (you can backup WhatsApp to Google Drive too for this).
But there is a little file that is deep into Android system folders that tells WhatsApp if it is verified and with what number etc., the key file, need to root phone to get to it, and they say it does not always work to copy that after a factory reset....(I think they say they prevent this in newer versions).
As for having a cloud-based number, I do have a UK Skype number, but it acts as a normal landline number, it can not receive SMS (as landline numbers can not), so that does not help. Interestingly I can send SMS using Skype credit, but not receive one.
Not sure about Magic Jack or Google Voice, I guess they can receive SMS... !