Can a MVA cause a blow to the skull or brain injury that would send pain through the neck, shoulder, hands, back and leg?

Yes. The distribution of your pain may be due to either injury to the brain but also to the cervical spine. A MVA can certainly be responsible for an injury to the spinal cord high up in the neck. This area is the location of nerve fibers that arise from the areas that you mentioned. See either a neurosurgeon, orthopedic surgeon or neurologist.