It would be...if it were actually happening.
A. Unless one of these police officers he's enlisted to deport persons actually sees someone crossing illegally, the only other way to determine if they are illegal is to detain them. To do that you need probable cause. Unfortunately for conservatives (at least at this point in time--I'm sure SCOTUS is about to change this), being brown isn't probable cause. Yet.
B. Probable cause gets you arrested and investigated. Thanks to Miranda (I'm sure this is on life support too), you're entitled to legal counsel if you're arrested. Being extradited back to Mexico or points southward--or northward for that matter-- will have to go through a hearing in front of a judge.
C. By this time, the accused is in custody of, usually, the municipal or county jail. They are the ones who hold prisoners for ICE, magistration, arraignment, arrange for further detention. Abbot's loyalty battalions and agents are out of the picture once they are turned over to the local authorities. The local DA makes the decision to proceed or dismiss the charges that created probable cause. Not the state AG.