I am still unsure on this one.
Atmospheric distortion is not the fault of the lens, and will happen with any lens regardless.
But my experience has been that there is indeed a bandwith of how mushy images turn out in similar situations of degradation due to atmospherics. In other words: some lenses seem to maintain a better rendition than others, and some lenses turn in a higher numbers of images that can be fixed to an extent with some post production.
If the atmospherics are really brutal, than sure: all lenses fail and turn in garbage. But in my experience, there is a grey zone where the lens does play a role.
The fact that the 800PF kickstarts many threads on atmospheric distortion while 600mm f4 lenses with or without 1.4TC rarely do so, should indicate that the 800PF is particularly affected by atmospherics
If you prefer to see things black and white though, than we can all agree that you best put your gear away on bright days after 11 am and don't pick it up again until afte 5 pm.
That will ensure that your lens will perform optimally.
On top of that, if you really want to get the very best out of your lens, avoid spring time and summer from may onwards, and shoot a lot in autumn. Teleconverters perform wonderfully in october, but ruin many shots in may.