The short answer is that it is possible. Veteran’s Disability and Social Security Disability are two different programs and each has its own requirements. Each has a separate application process and should be completed even if you are already on one of the programs.
Interestingly, you may qualify for Social Security Disability while on active duty with the military. The reason is that Social Security Disability is based upon your ability to work, not whether you are receiving a paycheck. You may be disabled, not working or on restricted work and still receiving active duty pay. This, in its self, does not disqualify you for Social Security Disability.
Under certain conditions your application for Social Security Disability can be expedited based upon a veteran’s disability rating.