Oh def don't worry about vomiting from not eating! Also, I'm more than sure that if you ask, they'll def give you an anti-emetic for your surgery - maybe ask for Propofol(SP) as your sedative as well.
I didn't have any invasive surgery, but I was put under when I had my Endoscopy. I couldn't eat for 12 hours for some reason but I handled it well. They gave me Ondansetron for nausea and Propofol is heard to have antiemetic causes. I hope everything goes well with your surgery tomorrow! You'll be in my thoughts.