No. No one with a USA passport will be deported. When he was in the Senate, he was gifted a passport for official travel.
Wonder if he's ever had it renewed. If it expires, you have to furnish documents all over again to renew it.
If it was proved in a court of law that the name he was using was fake and his nationality was fake, what to speak of parents’ names and place of birth are fake - which it can be, and hopefully, will be - then that takes it to a whole ‘nother level.