Yes; extradition for any purpose other than trial, sentencing or to serve a previously imposed sentence would not be lawful.
In relevant cases, the courts in this country have been given assurances that the person sought will not be subject to the provisions of the President's Military Order No. 1.
Once the Extradition Schedule to the Police and Justice Bill becomes law, providing the Opposition amendments are removed, and the US President ratifies the Treaty, then the Treaty will come into effect immediately upon both Governments exchanging instruments of ratification.