Yes, that's quite possible indeed. It's highly likely your son is texting that person over iMessage, whatsapp, viber, Skype or any other messaging service over Internet.
By doing so, your carrier is not charging him or you for texting as this is not taking place over their SMS service.
The only way to know who you're son is texting is by asking him or checking his phone, I suppose.
(or if you're working for the NSA, you could check into his online data
)