No, the edge comes from the fact that ties aren't pushes (as I said earlier), but they are treated as wins for the dealer.
Once I get back to a real net connection, I'll find out what the edge really is. Playing as dealer makes a lot more sense if there's an edge.
(Edit March 15, 2008: Mooski, a local poker room manager, tells me that the house edge is 1.5%, and implied that playing as dealer at no-commission is a 1.5% edge for the player. That sounds about right.)