If a specific Exalt, Exigent or otherwise, were judged by the Immaculate Order to be Not-Anathema, how portable is that status?

Can Exigent Englebert, having been judged by the Immaculates to be holding up the Order and not threatening the status quo, then go to another satrapy with some sort of badge that he can flash to the local monastery that suggests he get the benefit of the doubt if any Exciting Incidents crop up? Or is he going to go through a full vetting any time he moves somewhere he isn't known?

Does the answer change if it's Solar Sally, with her caste mark...