What happens if a recruit brings a prescription to basic training that wasn’t declared at MEPS?

If it's a new one, then let those at the reception center know what it is for, and why it wasn't on the list.

All depends what it is for. It if is an antibiotic or antifungal that you need to take until complete, you have to finish it. Take his med to your recruiter and discuss it with them. If beyond that already, ask to speak to medical at reception. If it is a medication that for whatever reason you have to keep taking, you have to disclose it up front and that being said, do not stop taking until you discuss with a medical officer. At a minimum they should be an RN, PA, or Doc.

You do not want to be caught with contraband. Period. Unless you like the idea of forfeiting your RASP contract. You will most likely receive an Article 15 and lose any additional contract schools you came with. Not to mention pay, rank, and possibly being sent home.