The Short Answer to this Question is No.
Thinking that a holding a college degree ultimately disqualifies veterans from potential unemployability claims is a common mistake many disabled veterans make. While each case for unemployability is unique, it is important to keep in mind that a college degree does not automatically rule out your chances for obtaining important benefits.
A college degree does not mean that you are promised a job in the future. Many other service-connected ailments may make it difficult for you to land a steady job.
While it is possible for many disabled veterans with college degrees to find certain types of work, many with specific service-connected disabilities--including mental health issues--often cannot work in particular environments (such as environments with loud noise, or requiring a substantial amount of physical labor). This is important to keep in mind for unemployability cases.
Even veterans with some minimal, part time work have been awarded unemployability. In South Dakota, a veteran who worked 30 hours a week as an auto parts salesman was granted unemployability benefits.