No, the whole purpose of having an independent 3rd party provider is to have a daily archiving and preservation of emails which stay in place no matter what is done later.
So if this is accurate, then unless this firm colludes with the IRS, then they’ll be able to get those emails.
Even IF the contract exists and was in place, they WILL NOT be able to get access to them.
It’s the way it works.
Betting the 3rd party provider performs multiyear archive service.
IRS retains current “six month” history.
IRS, on a rolling basis, sends the “seventh” month out to an Iron Mountain or some service for long term Archiving