Is it possible to get genital piercing done under general anesthesia or should I just take a local?

Sorry! But if are nuts enough to get your genitals pierced, do not compound the potential complications with general anesthesia. Local anesthesia is all you should need. Better idea: don't pierce the sensitive areas...Ever! no need.
Local. Do it under local. General anesthesia requires a lot of equipment to monitor your heart and breathing. It also requires the services of a doctor or crna in a hospital or medical office. Doing a piercing under general anesthesia is unnecessary and the anesthesia itself would cost several times more than the piercing alone. Local is sufficient.
Local. I would be difficult to get anyone to give you a general anesthetic for this procedure.
Think Twice. Why do you want to do this to your body? Please see a spychologist and try to find out why you want to be destructive to your body and why you would want to inhibit and organ that was designed to give you an ultimate pleasure and gratification. Please think twice and see a competent professional. Don't be influenced by your peers. They may not be there tomorrow but your piercing will.
Why? General anesthesia will not be offered. Ga needs to be done under the care if an anesthesiologist. If you feel the need to get your genitals pierced then feel lucky if you even get local anesthetic. I have never heard of any anesthetic being given.
Genital Piercings . Are not done under general anesthesia. General anesthesia is used for medical procedures. If you pierce through your glans penis it may interrupt flow of urine. If you are not circumscribed it can prevent the foreskin from falling back into place once retracted. Penile rings can cause erections that do not resolve and require emergency medical care. An infection from your piercing can travel.