Possible, but uncertain. It depends on whether others related to your grandfather through his father have tested, the quality of their documentation and whether they are willing to collaborate with you. You may want to do both YDNA and autosomal testing to improve your chances of making a connection.

I was able to help a cousin determine her birth father, a member of my mother's family, through autosomal testing and comparison of our match with another individual from that branch of the family.

Here is a resource on using DNA in adoption; the process is similar:

http://www.isogg.org/adoption.htm

Jim