As one who served his time in the US Military (1981-1989), if the Lt. had requested to resign before he/his unit recieved those orders to deploy, then at the very least he would have been placed in "Administrative Hold" status until everything was sorted out, which would have made him ineligible to deploy at that time.
There would be a good 75% chance of the request being granted if his unit had not already deployed by the time the decision was made.
Even if it had, there still would be a ~50% chance of it being granted, with a near 100% chance of being assigned to somewhere other than Iraq/Afganistan, since he declared his conscientious objection before recieving orders.
There have been a number of officers and enlisted that have done exactly that since the beginning of combat operations in Afganistan in 2002, and over 95% have been simply reassigned.
If you wait until you/your unit recieve orders, it is clear that you did not object to the war, just to your personal endangerment, and that gets NO sympathy or understanding.