I have had lots of broody hens, and some do sit tight on the nest, especially if they think you are around, but I have watched from a distance, and most do actually come off to eat and drink, maybe not every day though. One in particular, I have been holding water up to her in this very hot weather, as I thought she could do with a drink. Usually though I leave them to help themselves, if in a hutch.
Once the eggs are nearly due, mine stay put, and definitely are not bothered about food.