The first apartment I rented in DC (12th and M) was rented more-or-less sight unseen. They were renovating our unit when we visited, so it was plywood floors, studded walls, etc. They showed us a unit that was a different size from ours, but recently renovated in the same fashion.
Everything went fine, but this was from a pretty respectable management company. If I recall correctly, we put down security deposit and one month’s rent advance.