885. ART. 85. DESERTION
(a) Any member of the armed forces who--
(1) without authority goes or remains absent from his unit, organization, or place of duty with intent to remain away therefrom permanently;
(2) quits his unit, organization, or place of duty with intent to avoid hazardous duty or to shirk important service; or
(3) without being regularly separated from one of the armed forces enlists or accepts an appointment in the same or another on of the armed forces without fully disclosing the fact that he has not been regularly separated, or enters any foreign armed service except when authorized by the United States; is guilty of desertion.
(b) Any commissioned officer of the armed forces who, after tender of his resignation and before notice of its acceptance, quits his post or proper duties without leave and with intent to remain away therefrom permanently is guilty of desertion.
(c) Any person found guilty of desertion or attempt to desert shall be punished, if the offense is committed in time of war, by death or such other punishment as a court-martial may direct, but if the desertion or attempt to desert occurs at any other time, by such punishment, other than death, as a court-martial may direct.
http://www.au.af.mil/au/awc/awcgate/ucmj2.htm#885.%20ART.%2085.%20DESERTION
Ok, so there you go, it requires the accused to have intent, which is a mens rea word. Interestingly, the article on AWOL does not have mens rea.
Now has for a defence of lack of mental responsibility aka, insanity. The Code reads as thus:
* 850a. ART. 50a. DEFENSE OF LACK OF MENTAL RESPONSIBILITY
(a) It is an affirmative defense in a trial by court-martial that, at the time of the commission of the acts constituting the offense, the accused, as a result of a sever(sic) mental disease or defect, was unable to appreciate the nature and quality or the wrongfulness of the acts. Mental disease or defect does not otherwise constitute a defense.
(b) The accused has the burden of proving the defense of lack of mental responsibility by clear and convincing evidence.
(c) Whenever lack of mental responsibility of the accused with respect to an offense is properly at issue, the military judge, or the president of the court-martial without a military judge, shall instruct the members of the court as to the defense of lack of mental responsibility under this section and shall charge them to find the accused--
(1) guilty;
(2) not guilty; or
(3) not guilty only by reason of lack of mental responsibility.
The accused carries the burden to prove their mental defect however as with most defences of mental incapacity and/or defect if one does prove the mental defect then other factors kick in such as capacity to be further employed. Now in this case of the alleged deserter, I doubt he's going to care if once he proves his mental defect that the military considers him unfit for duty and tosses him, but in the case of a lesser offence where the accused wants to remain in service, it could prove their undoing (but then if they really are mentally defective or diseased of the mind, they aren't going to really care.)
As for an immigration hearing, I would suspect the clause that is affording the application for refugee is the proposed death sentence, if found guilty of desertion during a declared war. Quite the political matzo ball for the immigration tribunal to have to decide if that were the case. To grant him his status as a refugee, would mean making a finding that the states are in a legal war and therefore he would be subjected to a harsher sentence should he be found guilty, to turn him down would mean they made a finding that there is no direct threat to his life should he be refused and returned to the US as there is no state of war.