Hi Donna-
No, I don't think you're going to get grandpa's DOB from your dad's SS application. Here's an article that pretty much sets forth what you will get.
http://www.ancestry.com/learn/library/article.aspx?article=9...Although it probably won't list your grandfather's exact DOB, check out your Dad's birth certificate if you have it. It might show the ages of your grandparents at the time of your Dad's birth. Mine does and many I've seen do. At least that will give you their year of births to play with.
Paul