I don't think that number is going to affect anything at all. (Then why do they include it? Welcome to the maddening world of financial aid applications.) I wouldn't put that you expect to pay full price if you are hoping to get some aid.
There are a few schools which do take need into account when you apply. They would be schools that guarantee to meet the financial need of all students who are admitted, but don't quite have the resources to do that without making sure they have some full-pay kids in the mix. This a very small group of colleges. You could call the school in question and ask what their policy is.
Here's a link to an article that explains "need aware" vs. "admit-deny," if you want to get a sense of how it all works: Colleges Where Need for Aid Can Hurt Admission Odds - US News and World Report