Is he unable to ensure that he will maintain continuous coverage or to surrender his plates now, before he departs for basic training?
That is correct.  He is unable to pay forward enough on his policy to ensure it would give him continuous coverage for the period he will be gone and he is unable to get to the DMV during business hours to surrender the plates at this time.
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?