You’re right, they don’t think that far ahead.
And of course that means we should prosecute them for that crime as well as Entering Without Inspection (Crime #1) when they are apprehended.
As for being “disruptive to training and morale”, I think battalions of unarmed ditch diggers, latrine cleaners, lawn maintainers and road repair laborers overseen by some of the meaner NCO’s would be quite welcome in the military to relieve the actual Americans from having to do those tasks. Letting them know that might be their fate upon arrival might be just a bit of deterrence: you may get drafted, but you won’t get a weapon and you won’t be doing anything fun.
Not sure what kind of discharge that would get you. Many would take a bad discharge over punitive service. And you won’t be digging ditches if you’re pregnant.