Can they use an official letter for personal guns?
On a different note, is there anything special that happens when the wait times hit 90 days? Does that affect the validity of the application?
Generally if they are buying a personally owned gun that will be used as a back-up or off-duty gun, or for patrol rifles, agencies will sign off and there is no wait.
It really comes down to individual agency policy.
The date of the application is not what is important; it is the date of the NICS check. Since you have to re-certify to your eligibility to buy/possess as long as you are within 30 days of the NICS you are fine.
I've not gotten any Not Disapproved faxes any more than a week or so past the NICS date yet.