can they make citizen’s arrests?
I dont know, but I would not suggest detaining someone over an illegal entry. One could be setting themselves up for a lawsuit. There are a lot of groups out there that provide legal help for illegals and a person could be sued or even falsely accused of something.
I dont even know if the border patrol would agree to take someone into custody if a group tried to hand over people to us. There would be questions about where, when and how the alien in question crossed the border or even if they crossed or maybe were caught in mexico near the border since in many places there is no barrier to indicate that one crossed the border.