[jandrese]

Usually if you can SMS verify they will let you in. Google (and many other companies) insist on SMS not because it is secure (it's not) but because it requires account spammers (scammers) to put up some money (buy a phone) before they let you use the service too much. I would be surprised if you get through the registration process before they insist on SMS verification if you are coming out of a VPN provider netblock. And forget coming out of a TOR exit node.

Keeping your identity hidden from Google while using their services is a fools errand. Find some other email provider with less big data mining expertise.