Yes a hen will sit on infertile eggs. If she decides to go "broody", she doesn't care if the eggs are fertile or infertile! I had one go broody and I already had several hens that had hatched out a bunch of chicks and I didn't want anymore chicks. It took me over a week of taking her off the nest, banning her from the chicken coop during the day, before she finally stopped trying to sit on an empty nest.
