I don't think he will need surgery, no.
With preparation and the right treatment, a herniated disk is a low risk injury for a player to endure. Sure, he'll have to pay attention to it his whole career, but who doesn't after a few years in the league?
Remember Pierce as a young guy was reluctant to tape his ankles? Maybe the process of paying attention to his body just started much earlier than most guys. Also, Sullinger is only 20 years old--I suspect he can at least last a few years without surgery.