If your Google account storage is full, you cannot receive emails. I confirmed this in the official help.

I didn't know what would happen after the 15GB that comes free with every Google account was filled up. I thought it would just mean I couldn't add new files to Drive. I was wrong.According to ...
Forbes

Gmail Account Lockout Hack Has No Fix — Google ‘Looking Into’ It

This devastating Gmail attack locks users out of their accounts with no comeback. Updated December 7 with more information regarding managing a Google Account with Family Link, the parental safety ...