According to the law, Illegals are still citizens of their parent country, unless they have a record of being caught, or comiting a crime. All the illegal would have to do is lie on their application stating that they never crossed into US territory.
Come on. Then all the military would need is a Passport and a visa. If they can’t produce either, TS, can’t enlist. Also if they SWEAR when they enlist that they are not here illegally, then THAT should preclude a path to citizenship if they swear falsely. It’s not rocket science or an insurmountable problem. It just takes the will to do it.