Just thinking about your situation logically, you are agreeing a contract to provide a tenancy to begin at a certain date. As long the EICR is in place before the tenancy begins you should be fine.
The Openrent boxes & expiry dates are just for marketing (ie Openrent reminding you about them). They don’t affect your contract in anyway. I wouldn’t move a tenant in until the electrical repairs are completed, but no problem with signing the tenancy in advance.