I think it depends on the development around the arena. Looking at the masterplan it doesn't seem like the complex itself would provide anything compelling that would interest out of town folks beyond the tournament games. Lowes, Walmart, Big Lots and a cash wash is not much of an attraction.
Now, if the project attracts other entertainment options close by, that would make a huge difference. I just don't see many people traveling from out of town wanting to drive into the city to do stuff and there's not much to offer in that part of Henrico in terms of entertainment.
The Green City location always seemed weird to me for an arena.
The tournament is the attraction. There was nothing to do during the CAA tournament outside of watch basketball but people showed up anyways.