I had to drink a bunch of water before the ultrasound for a CVS (chorionic villous sampling), another prenatal, genetic test. It's done much earlier than amnio. It was so my full bladder would push the fetus up to a place that was easier to see with ultra-sound. I thought for sure I was going to pee myself. I told them, so they said to go to the washroom and squirt out a little bit and stop. Much to my surprise, I actually managed that.
They couldn't get any results from the CVS, so I had amnio a month and a half later. They didn't ask me to drink a lot of water for that. By then, the fetus was in a better position for viewing with ultra-sound.