Zactly.
Anyone who is not a Citizen or permanent resident is a transient alien, at a minimum...
They cannot be conscripted into war and are therefor not under the jurisdiction of the United States, in that regard, otherwise they would be a full citizen.
Further, the United States cannot represent them in foreign affairs with Kings, Potentates, Ambassadors or even at the Embassy level, to petition for relief of any sort for a citizen.
That responsibility and purview would remain with their country of actual citizenship. Only their government could represent them...
Oops!
September 25, 2014:
A small number of undocumented immigrants in the U.S. will have an opportunity to join the military for the first time in decades under a new Department of Defense policy unveiled Thursday.
The new rules will expand an existing program allowing recruiters to target foreign nationals with high-demand skills, mostly rare foreign language expertise or specialized health care training.
For the first time, the program — known as Military Accessions in the National Interest, or MAVNI — will be open to immigrants without a proper visa if they came to the U.S. with their parents before age 16. More specifically, they must be approved under a 2012 Obama administration policy known as Deferred Action for Child Arrivals, or DACA.