Sure, you can ask to be awake through any procedure or surgery. It doesn't mean that they'll let you, many times it is denied because you'll move. Having a patient jumping around during the procedure can be deadly
I woke up during my first one and I asked to stay awake so I could see what was going on and they let me. I just had to tell them if I felt any pain, which I didn't. When I woke up for the next one they put me back under right away. I just tell them now if I wake up leave me awake but comfortable.
Yeah... it's not so bad. I was awake for mine... NOT by request though! They gave me 2 X the "normal" amount of sedatives, my blood pressure dropped too low, so I had to go through mine awake. Not a big deal, really. The endoscopy (tube down the throat into small intestine) was much worse!