No. No 1A suppression here and no 5A due process right to his press pass nor does he have a property interest in it for purposes of the Takings Clause. He battered a woman on national TV. That is what this is about. No right to be on WH grounds (privilege, think DL), no property interest in press pass (privilege, think DL).
Yeah he thinks he owns his press pass. Judge will set his ass straight. Three judges (it'll be appealed) will set his ass straight and SCOTUS will deny certiorari (because his ego is that large to try to go to SCOTUS).
Leftists will descend on Tennessee like locusts. "Our taxes are too high so we move to low tax states and vote to raise our own taxes, then bitch and moan about them." Stupid.