On the original topic, of course there can be an illegal merc. That's a pretty silly question. Your actions mean more than your ID. Especially as a merc.
I've recently taken to writing more RP around my characters. At least I've been trying to when I have the time. I'm finding it very helpful. Because the game mechanics tend to oversimplify things sometimes, writing RP helps give a more accurate picture of what things really look like.
Places like Pittsburg and California Minor are small bases. Small as they are, I imagine that in reality there would be a lot more traffic coming and going in orbit. It would be easy for a ship that has managed to keep a somewhat low profile to sneak in there to make some quick repairs and leave just as quickly. That is provided the pilot has not become so notorious that his name is known in every port in Liberty.
It's all about being smart and prudent. You don't dock when the law is chasing you. That's foolish and you'd be dead before you got out of your ship. You don't stage your attacks from places like this. It wouldn't be too hard to figure out what is happening and the administrators of the port would shut you down because they don't want the kind of trouble you bring.
This doesn't solve all the problems, but for me it's a start. I try to get a better idea of what things actually look like and then I can approach things from the perspective of what a situation would actually look like and not what I can get away with in terms of game mechanics.