Yes but they can charge him with 8 USC 1326, Unlawful reentry after deportation. Its a slam dunk charge because they is no real defense.
There are automatic enhancements tagged on to the sentence based on past immigration violations and criminal history.
Given his past I would guess he would get 4 to 6 years to run consecutively along with his federal weapons charges.
This is all wrong. He can be charged with the federal offense of being a felon in possession of a firearm. The concept of double jeopardy is not applicable.