Depends.
SPOILER;
If you choose to let the chick lie and say that she got the blessing and so on so forth, I have no idea.
I chose to not let her, and she attacked me. So I killed her (obviously). Tried taking the axe, no dice. So I went back to the Hall and told the guy the truth. He told me to leave and never return, even though he understood my view and didn't blame me for it. I'm fairly certain they won't aggro if I return, however, because I waited and stayed there for a few in-game days, as well as left and came back inside a few times. So essentially you get to use the Mead Hall. That's.. about it.
EDIT: Weird how I couldn't get the spoiler tags to work.