About 2 1/2 years ago my then 13 year old cat, Midnight, needed to have her teeth cleaned, and several teeth also had to be pulled. The first thing that happened was that she was given a physical and pre-anesthesia blood was done to check the function of vital organs such as the kidneys and liver. During the actual dental procedure, the vet used a gas anesthesia which he said was safer to use for Midnight, due to her age, than an injectible anesthesia. I called to check on Midnight a half an hour after the procedure was completed and I was told she was already sitting up in her cage. When I picked Midnight up later that same afternoon, she was fully alert and there was no indication whatsoever that she had ever been under anesthesia. I can't remember the name of the antibiotic that was given, but Midnight was also able to take the entire 10 day course without experiencing any problems.
I agree with Sandie, if you have some concerns, the best thing to do is discuss them with your vet.