How about wearing a jacket or a polo shirt with the name of your theological seminary blazened on it, when walking around town. Would that set you out as likely a pastor? Would that be a good modern equivalent? Some seminaries sell those.
Well some of us would not want to be associated with our seminary of record.
But seriously interesting question. Should Pastor's "set themselves apart" in daily life?
I can sympathize with your feelings about PTS, but even then, it could lead to some opportunities if you run into someone who is mainline Presbyterian or Methodist, and others won't know the difference to distinguish it as a "neo-orthodox" school. My school, GCTS is not that, but it's still pretty broad. Yet I would probably sport a shirt or jacket of theirs around, since most people, if they have heard of it at all, would still associate GCTS with biblical conservatism, even Reformed theology.
In answer to your question, probably, if it could lead to opportunities. It would be nice for people to know that a pastor is there if they need one. And you would want them to talk to you, wouldn't you?