Yes, he'll be fine. He'll probably be very sleepy when he comes around. We noticed that Pitch was too tired to notice when she came round if Putt was there or not, when she got home Putt snuggled up to her then.
He'll soon be back with his piggie pal.
Each piggie reacts different to anesthetic - He may have little shakes, don't panic this is normal after anesthetic. Put some of his favourite food by him, maybe some watermelon or cucumber so he can get moisture without having to go over to the water bottle. Weigh him also and keep a eye on his weight so you know if he's eating or not. You may have to syringe feed if he isn't. Check he is pooing also. Depending on what the vet has done (filing teeth) he may need some metacam (painkiller)