Do deployment orders actually come from the president, or from some officer in the Army? Even if you admit Obama is not legally the president, does that absolve you from the requirement to obey orders from your chain of command?
If you think the colonel two levels up in your chain of command is somehow not legally qualified to command, can you ignore orders from your immediate superior? "Alright men, attack the enemy." "Sergeant, I think the colonel cheated on some of his West Point exams, so I can't obey that order."
Hey, maybe I should stop paying my federal and local taxes because I can't see Obama's birth certificate. I wonder how that would work out?