What is the risk of waking up during surgery?

If you are undergoing general anesthesia with an anesthesiologist, the chance of waking up during the surgery is quite remote.  You should discuss your concerns with your surgeon and the anesthesiologist ahead of time.

My
approach to avoiding anesthesia awareness is to avoid general anesthesia. Our
patients undergo Twilight sedation so that they are breathing on their own and
in a dream state. We use versed which causes amnesia. All of this avoids the
worry of a patient waking up from general anesthesia with a tube down their
throat and panicking.

I would definitely relay your concerns to your plastic surgeon and your anesthesiologist.  Although this has been reported, it is very uncommon for this to be the case.

Anesthesia Awareness is very rare, some think it does not exist at all. In over twenty years of doing breast augmentation surgery I have not seen a case. I did have one patient who gave a pretty good history of anesthesia awareness with previous surgery. For the surgery I did with her, the anesthesiologist noticed that she did require more medicine than what would be expected for her size. So she was given a little extra medicine during her breast augmentation procedure. For that surgery she had no recall. I think as long as you have a good anesthesiologist, it should not be an issue. The medicine we use for breast augmentation is not the type that can leave you awake and unable to move. If you are getting light, it should be noticeable before you are awake enough to be aware. Let you surgeon and anesthesiologist that this is a concern for you, and it will make them more vigilant and you more comfortable. 

This should never happen. We have never had a single incidence in 17 years using Board certified anesthesiologist under full General anesthesia