The answer to your question is probably. But I think it's very important to understand that I don't think this is really the question that you ought to be asking...
The better questions are these: Is doing a Brazilian Butt Lift on me under local anesthesia in my bests interests? Is it safer? Am I as likely to achieve my goals? Why is it your impression that local anesthesia would be better?
The answer to these questions is NO, I do not believe it is in your best interests.
Here's the problem... Obviously if you were to pursue a procedure to improve the shape of your body you would be doing so in the hopes of achieving the best outcome possible- in other words, no one ever goes to a plastic surgeon and says, "I don't really want your best work, maybe just mail this one in..."
Trying to do a procedure of this magnitude under local anesthesia is in my opinion a mistake because even with a very good block, you are probably still going to have some pain during the procedure- and when you do, it will cause you to move a bit. The combination of you having difficulty holding still and experiencing pain is going to make it much harder for me to do my very best work for you, as I worry that you are hurting and having a bad experience, and as I try to complete the procedure on a moving patient...
So, in terms of you having a positive experience and achieving your goals, I think you are much better off under general anesthesia for this procedure.
As far as your safety goes, again, I would recommend general anesthesia. Many people (including a lot of doctors) believe that local anesthesia is harmless and totally safe... but the reality is that it can be a great risk to your safety- especially when given in the large volumes that would be necessary for you to have this procedure done. Indeed, recently a woman in Florida died while having a non-plastic surgeon perform liposuction on her under local anesthesia. She died because as she kept complaining about pain, he kept giving her more local anesthesia. She eventually became toxic and died.
For healthy people, the risk of general anesthesia is very low and manageable when administered by qualified anesthesiologists.
I think that if what you want is to be as safe as possible, and to have a pleasant experience, and the most beautiful butt possible, trying to do this under local would be a big mistake.