I think autofocus accuracy may well contribute to some loss of sharpness at long distances. I adjust all my TC+lens+body combinations that have fast or moderately fast apertures before I use them. Another matter is simply the lens MTF. A higher MTF lens may tolerate a bit more atmospheric degradation before the image quality imperfections become visible in the image. Also a higher MTF lens may work better with a TC again leading to satisfactory image quality even in the presence of some degradation due to distance and atmosphere.
As for Nikon service calibrating the AF, it may be a good plan a) if you only have a few items to calibrate, or b) in some extreme cases where the camera or lens is way off typical, and c) if you have a service facility nearby. However I cannot give away all my camera bodies and TCs to service every time I add one lens to the kit (so that the bodies could be adjusted by Nikon to focus with the lens properly), or give all my lenses to be tested when a new camera is added and adjusted (not to mention if they adjust the lens, all the cameras will have to be adjusted as well, and may lead to problems when selling the lens for use with another camera). The equipment is purchased for my use, not for sitting at service. I prefer to adjust the combinations that I have myself with testing in my applications. it usually leads to satisfactory results or at least better than out of the box. I realize that service facilities have more adjustments that can be done than the user (and perhaps better techniques for measurement) but there is a trust issue with that approach. If they explain what they are doing, why they are doing it, and how they are doing it and I can monitor the work as it is being carried out and give my input to the process then ok, but I'm afraid this is more access than they care to give me.
OK. Having had lenses and camera calibrated by Nikon service, they filled me in on how they do it. If your lens is out of calibration, they can actually reset it
in lens and there will be no need to have a calibration amount in your camera's AF Fine tune settings. So, if your lens needs +5 they can reset the lens to suit a +5 setting but actually show zero in the camera's AF Fine tune settings. In other words, there is a re-calibration that can be done in the lens. However, Nikon would rather you send your camera in as well for calibration as they will adjust your camera body with a reference lens so as to have a starting point and get your camera correctly set. If they do not get the camera set correctly, then they will forever be chasing their tail trying to get lenses set correctly for any other body that you may subsequently bring in for calibration. By this, I mean there is no point resetting your lens in the
lens's memory to suit a particular camera as the next camera may require the lens to be something different. It is therefore best to get the camera set to a known reference point, using a reference lens that they use to achieve this. After they calibrate your camera to that starting point they will then effect calibration to your lenses.
Now as for the belief that TC's work better with fast lenses, I fully agree. However, my 300 f2.8 VRII is a fast lens and yes it does work better with TC's with less IQ drop, but it still suffers from distance related IQ drop as did my 500 f4 VR. Having talked to other users of Nikon super tele lenses and using TC's, they also notice a drop off in IQ at distance. No, it is not an AF Fine tune issue as we have all AF fine tuned our lenses.