He volunteered to go to Afghanistan for the distinct purpose of filing this suit. If you doubt that, you can go check out freeper land where he telegraphed his punch.
Can the Army smack him over this?
I don't think he's violated the UCMJ. However, there are communications from Cook to Taitz (the incompetent birther lawyer that represented him) from February where Cook indicated that he wanted to join a suit as a military plaintiff against the Obama adminsistration. This was prior to May where he
volunteered for deployment. This means that there are likely some questions as to if he volunteered only to lodge a suit against Obama. I don't know the exact reg, but that strikes me as piss-poor officership.
I have my doubts anything will happen to him. More than likely, he will return to where he came. His next evaluation will suck, and he'll retire.
That's just my gut. It's piss-poor officership to use your rank to try and prompt a constitutional challenge. It's the antithesis of an apolitical military, and I don't care who the President is.
It would be akin to an officer challenging Bush's authority to deploy soldiers due to the 2000 election results.