It's not up to the president, it's up to the command of each branch. For instance Air Force does not accept conditional permanent residents for enlistment, but Army,Marines, and Navy do. If the Army wanted they could even allow an undocumented immigrant to join, but that would be an extreme case! But generally speaking you need to be a legal permanent resident or U.S Citizen. On another note I am in DEP right now for 12B/Combat Engineer. 3 months ago I was EWI and now I'm in the Army