Basic training is not a deployment.  The DMV does have a procedure in place to exempt military personnel from the requirements, however the procedure pertains to returning from deployment.
What would happen if his NY State registration would expire while he is on active duty?
Registrations are extended for up to 60 days from return to NY State.  This extension applies only to vehicles registered to military personnel.  He would need to show proof of military service or separation.
Is there another resource I could use to get more information?