I've heard some people say they had a problem with deer eating their sunflowers prior to putting on a head, not sure if they actually eat the flowers. We planted several acres this year and last and have not had any issues, but we have corn planted next to the sunflowers, so maybe that helps.
That being said, I watched a hunting show a few weeks ago where they were actually hunting deer over a huge sunflower field, somewhere in Kansas I think.
So, yes, deer will eat some part of the sunflower plant.