Yes he will. Look at the post 72 above.
The facts surrounding Maj. Cooks ordered deployment are dissimilar in almost every what from the facts surrounding this physician's deployment. Cook was an reserve officer who volunteered for deployment. Then, a month or two later, he files a civil suit for a TRO (could have been injunctive relief, I can't remember anymore) to stop his deployment. The Army took it as a de facto request to withdraw his voluntary orders. As it turns out, officers who volunteer for duty, can withdraw their submission up until the time they're deployed. The Army granted that de facto request, rendering the civil suit moot.
This is completely different, as it appears that this is in a involuntary deployment order. The soldier can't refuse involuntary deployment orders, so there's no de facto request that the Army can acquiesce to. In short, they're painted into a corner with court-martial as the only way out, assuming the Capt actually doesn't report for duty.