My dad was a psyd in the army for 23 years. He was probably the least high speed person I've ever met. He never did any extra schools, and still was offered numerous times to be the mental health provider for various special forces units. Never took them up. Right before he got out, they were about to force him to deploy with a ranger unit in some new initiative to have mental health support more easily accessible. I would say that the army is more concerned that you're a good shrink, not that you know how to run and gun. If you want special ops opportunities, they will present themselves even without extra training, so long as you're good.