How to pause throttling and blocking of out-of-date on-premises Exchange Servers

Can I ask we are planning to have exchange not send email. Currently we want to go to all cloud. Our mail is office 365. Its basically just smtp going from exchange. We are fixing that with microsoft office 365 suggested methods.

My question is if we remove our exchange server from the internet basically and office 365 entirely. We do need more time to resolve this for our school. Can we still use it internally just to manage the odd permissions? We basically just use exchange on prem to create accounts with mail attributes into a local AD environment and then use AD sync.

I am hoping if the exchange server is removed from external network and just use it internally for permissions this change wont hurt us if the exchange server is not sending mail and not attached to office 365 connector anymore?

Thank you.