You can download the USB spec, they have drawings with measurements, I just looked at them. In the Type "A" receptacle the tongue fills exactly 1/2 of it, the bottom edge, where the connectors are, lies exactly on the vertical centerline of the socket.
The board on the end of the plug can be between .38mm and .51mm thick and sits below the plug tongue when connected. So if the plug has a completely central tongue which is a full .51mm thick it would have to bend by 0.255 mm to slide underneath. That is around 2 degrees of bend, less if the plug tongue goes extra far into the plug and only even that if the socket were entirely rigid and kept the plug absolutely perpendicular. Mine (unscientifically) slop up and down a few degrees.
The socket tongue has a .38mm chamfer on it at a minimum angle of 28 degrees, the plug tongue also has a chamfer of the same angle, that's enough to guide one piece under the other.
I doubt it will be frictionless, but there's certainly enough room on the standard Type "A" socket as specified by USB to have a thin, central tongued reversible plug make contact with a small bend of the tongue.
Also worth pointing out is that any design which carries the USB mark must pass insertion, holding and removal force tests as well as contact resistance and capacitance tests to ensure the connection is good.
Figures 6-7 (page 95), 6-9 (page 99) USB revision 2.0 spec.