Normally he will be treated and returned to duty. The reason he has stones though may be grounds for medical release but this would be HIGHLY unlikely.
For the most part would have stoned removed, or pass it on his own, and as long as there were no complications would be back to full duty in no time. Some duties would require further studies and a waiver (sub duty).
I have had kidney stones for 10 years now and still on active duty. Kidney Stone- ER Visit, IV-Pain Meds sent home- Back to work next day- Wait for next stone to pass.
He will be treated and will continue his navy career no doubt for one reason... money. they navy spends crazy amounts of money on each new sailor for training, housing, food, etc. to kick him out for something as easy to take care of as a kidney stone would be against the military's "fraud, waste, and abuse" policy. kidney stones are actualy pretty common in people just out of bootcamp. im stationed at marine corps recruit depot as a staff corpsman and we see kidney stones quite often as a result of their diet here. we usualy just make them pee it out and they continue training.