No matter what you use for hosting, make sure your email address is on a domain name you own.
Having your own domain gives you a lot of options to move your email around to the best deal and hosting at the time, companies are going to come and go and if you utilise free email a domain in front of it will avoid having to change 500 accounts on the internet when you inevitably have to move.
But in any case, Google shutting you off is much more likely than your registrar doing so.