No. The Social Security Administration (SSA) has different policies regarding the approval of disability benefits that are much different from the Veteran’s Administration policies.
The SSA requires that you be 100% disabled to receive benefits. The Veteran’s Administration has a percentage system. The VA, for instance, may pay you for a 50% disability while the SSA may not.
You’ll have to apply for benefits from each agency separately. There are cases where you may end up with two applications in at once, one to each agency. The approval of one agency, however, will not guarantee the approval of the other.