There is always some risk with anesthesia, but most pigs do just fine. If the vet is able to take out the abscess completely (walls of the capsule and all), that will fix the problem and is the easiest outcome to deal with for both you and your piggie (just lancing and draining the abscess requires a lot more aftercare.) One of my pigs had an abscess removed completely off her lower back and it was the easiest abscess I've ever dealt with!
For what it's worth, there aren't guarantees, but I've had pigs go under anesthesia six or seven times, as well as a Syrian hamster who had repeat anesthesia for dental issues, and they all did fine. I really do think you are doing the best thing going forward with this operation. Best wishes to you and your piggie!