So, suspecting someone of being an illegal immigrant is enough for a Terry stop. That means providing ID is required. If ID is not provided, that's a secondary charge and requires further investigation however almost everyone talks, gives their status. The second someone admits to not being in the US legally, the due process ends. There is no reason after admission to see a judge, or go through a hearing. It should be straight to a plane. Document the admission, fingerprint etc. And goodbye.