Surfing yes. Checking e-mail, no. They even talk about this in their docs. If you use an account that is tied to you you aren't getting the same kind of protection that TOR was designed for.

You can sign-up using the Tor Browser with a web email service that allows Tor (such as tutanota.com) and hence your identity won't be tied to that email (unless you leave personally identifiable information, email is unencrypted by default so don't forget about that).