chess.com doesn't know you deleted the email so that should be fine....you should probably link it to a new email after you log in though
Keeping an Account After Deleting Email

Hi,
If I delete my email account, would I still be able to log in through my chess.com account? (Signing in directly with your chess.com username and password)
Yes, as long as you have a password and aren't logging in with that email. That said, you should disconnect that if you have it connected in settings and if that is your contact email, change to one you currently have.
Hi,
If I delete my email account, would I still be able to log in through my chess.com account? (Signing in directly with your chess.com username and password)