Hi, Joking,
Being "put under" is a normal procedure now. If you are thinking of the type of anesthesia where you will be put to sleep, during the surgery, it's very normal.
There are considerations, that you can discuss with your doctor. If you are on oxygen, 24 hours a day, there are more precautions taken, with just a little more risk involved.
But, if you are a "normal" person, breathing OK, with no heart or lung problems, you don't have much to "worry" about.
Please discuss this with your doctor, and I am sure he/she can assure you that you will be fine, coming out of the anesthesia. Also, you will probalby have a different person administering the anesthesia, and he/she will also talk with you.
Here is a link explaining much about breast implants/surgery, with many other links for good information:
http://www.justbreastimplants.com/
Personally, I think a woman looks GREAT naturally. But, that's just my own opinion.
I do wish you the best, and please talk with the doctor, so he/she can give you a "peace of mind" about waking up.