Jon, I don’t have any hard data, but when we were racing in IMSA the factory paid a lot of attention to it. The Ford engineers always told us to run 3” of clearance around the tire to minimize tire shearing.
A rotating wheel is a big pump and if the tire is too close to the side, then you have still air against the tire tub and the tire sliding by that air. If the gap were more instead of less, it seems to me there would be less "shearing" of the air and less drag. This is true in incompressible fluids and I don't see why it wouldn't hold true in air.
In our case one side of the tub was partially open to the air stream ad in your case you would have a fully enclosed tub, which might make a difference. It would be interesting if some of the stream liner or aero guys would chime in. Tony