It also has an impact on when the mesh disappears as you zoom in on it. (Is that the "clip radius" mentioned above?)
Sort of.
Here's how it works (or at least my understanding of it

). When Orbiter does an external render pass, it considers all objects in the scene, their distance to the camera and their respective clip radii. Orbiter adjusts the camera clip plane distance so that it does not intersect any clip radius, but with a minimum clip plane distance of 2.5m.
For example, consider a scene with only one vessel in it. It has a mesh 10m long and the clip radius has been set to 2.5m. This mesh will always be clipped, no matter how far away from it you get*. Now introduce another vessel to the scene that is closer than the first one. The first vessel's mesh is now not clipped because the clip plane distance has been shortened to accomodate the second vessel.
The minimum clip plane distance of 2.5m means that if you get within 2.5m of any part of a mesh, that part will be clipped. This cannot be changed (except I think Artlav had a hack, ahem, plugin that reduced the minimum clip plane distance). The minimum clip plane distance for internal render passes is 0.1m, so that virtual cockpits are rendered with little to no clipping. This comes at a framerate cost.
BTW, spacecraft3 addons cannot set the clip radius size. The clip radius is set to Orbiter's default, ie, clip radius = size.
* Perhaps there is a limit, there is no mention of maximum clip plane distance in the documentation. If there is a maximum, it is quite long, as I discovered when working with Ananke.