I think the nails need to be a certain length, but I've worked with women who had nail polish on and it was okay. You have gloves on most of the time anyways.
But they might get messed up quickly since you'll have your hands in water and extreme heat sometimes. So that's something to keep in mind.
So I just got acrylic nails/gel polish.... I work in the deli. Is it against the dress/Health code?
Why didn't you just ask this question BEFORE you went and got your nails done?
I can tell you one thing, nails are one of the nastiest places on your body. If you have long nails I would scrub them with a nail brush and wear gloves.
If you're touching food you should have gloves on anyway, and my former dept. head always had long acrylic nails and they had no problem with it. you should be fine.