No, it only indicates that you belong to an NPC faction.
As for being 'unprotected', it will wear off after some time, or if you die in the city.
Players can attack you freely while you're unprotected.
You can check if a player is unprotected by standing next to them, holding alt and
left-clicking on them, and choose 'Push'.
If you get a message saying "This person isn't blocking anything yet." - They are unprotected
If they are knocked down, they are unprotected because of blocking a doorway.
Neither of these means the target is protected in this town.