Oh sure the appeal is automatic but the grounds they'll be looking for in overturning concern improper courtroom procedures or actions of the court officers in the disposition of the case, not on the evidence (unless tainted) results or sentence.
Lets take a look at the MCM.
To repeat - "Error prejudicial to the substantial rights of the accused."
We see that Judge Lind can be challenge on appeal about her decision to not allow any witnesses and evidence under the very liberal rules of discovery of UCMJ Article 46. In my post 580, it has been reported that witness 5 for prosecution introduced Lakin's motive to why he chose to miss his mandatory flight and missing movement. Obama's eligibility is now fair game.