Kind of... yeah.
Like, occassionally they show a panel showing the sword or the hat by itself... like an establishing shot to show where it is, even if no one is around it and there is no danger. But in the case of the sword (and Tyrese's hammer) they show flashbacks to their actual origins:
In the comics there are instances where she is seperated from the sword and the story will just continue following whoever is holding it. And with the hat, at first you think of it as Rick's hat... then he of course give's it to Carl and after awhile you think of it as Carl's hat, not Rick's anymore... but I'm at the point in the comics where its neither of theirs. A character you guys haven't seen yet has it, but its still there all tattered and wartorn. Its not really anybody's hat. Its just
the hat. Like any of the other survivors. One of the other iconic weapons even has its own name, so it is refered to by name by the characters when they are talking about it instead of calling it an object.