Absolutely not! An ICE agent is not an officer of the court. That why they are accompanied by local, county, federal, and state law enforcement. Those officers carry legal weight from the courts.
It’s like when a bill collector calls you. Then tell you that they are going to sue you. They are in violation of the law for practicing law without a license. Or if they tell you that they will arrest you. They are impersonating a law officer.
So actually, ICE agency should not have power over no one but their own behavior.