There is no grace period.  If you have not been issued an EFIN, you just can't e-file, period.  Nothing Intuit can do on that front either.

What Intuit meant is that you can still use ProConnect to prepare and print returns.  Practically, anyone can subscribe to ProConnect (Intuit will take their money all the same), just that only those with a valid EFIN can use it to e-file.

Assuming you are otherwise required to e-file, you are not supposed to be able to use waiting for the issuance of your EFIN as the reason to file on paper.  But your clients can always opt out of e-filing, if they so choose.