Leaving aside the issue of the guilty plea, SCOTUS does not have jurisdiction of this case, and may never get it.
A military defendant convicted at a court martial has a right to appeal to the Court of Appeals of that branch of the service (in this case, the Army Court of Military Apeals). If that court upholds the conviction, the defendant can ask the United States Court of Appeals for the Armed Forces (CAAF) to hear his appeal, but that court's jurisdiction is discretionary; they can refuse to hear any case without giving any reason.
If the CAAF refuses to hear the case, the case is over and there is no right to even ask SCOTUS to hear the case. Only if the CAAF agrees to hear the case, and then upholds the conviction, is there a right to ask SCOTUS to hear the case, but there again, SCOTUS's jurisdiction is discretionary and they may refuse to hear the case without giving a reason.
I figured Danae knew this...as most of us do.