Check the available AF sensors for the D4s, D5, and D500 with the 600mm f/4 and with the addition of the teleconverter as the outer AF sensors are not usable.
There is a big difference, particularly with D500/D5, between
no outer AF points available (what you imply) and some cross type AF points being restricted to single line detection which is what you get with outer cross type AF points on a D5/500.
On a D5/500 outer AF points are reduced to single direction detection with some long focal length lenses even when operating at faster than f5.6.
How many and which cross type sensors are reduced to single line detection is explained on pages 98-101 of the instruction book. Those considering a D500 can download or view the instruction book at many Nikon websites to check AF point availability with a range of Nikon lenses.
With the 600 f4 (the lens being considered) with no converter on a D5/500 the two outer extreme column of cross type revert to single direct ability, and with a 1.4 converter the two outer blocks of cross type revert to single direction.
On a detail all outer AF points on the three cameras you mention work with f5.6 combinations to Nikons unspecified minimum standard.
Going further with some limitations as to when and what with all Nikon "official f5.6" AF points often work quite well with f8 combinations and stationary subjects - though usually well below focus tracking speed needed for birds in flight.
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Leonard Shepherd
You can buy kit. The rest is mainly down to you.
The more you practice, as with a musical instrument, the better you are likely to become.
