You can't buy another stop of light. If I needed the range i'd put my long lens on a crop body.
Firstly, this lens is reportedly 461mm long, and to be only about half as long as its focal length, it must have diverging rear elements (as all true telephoto designs do) giving almost 2x magnification of the image produced by the front elements. So it roughly resembles a 400/2.8 front part married to a 2xTC.
Likewise the 456mm long 600/4 must roughly resemble a 400/2.8 married to a 1.4x TC.
So how would using this 800/5.6 on a 35mm format DSLR of a given pixel size compare to
- using a 600/4 with 1.4x TC or a 400/2.8 with a 2x TC on the same body.
- using a 600/4 with no TC, with a sensor of about half the area and similar pixel count at half the ISO speed.
[Edit:] Adding a second smaller format body to your kit might be cheaper and lighter than adding this lens! Actually, this is my attitude to all long lenses slower than about f/4: I would rather use a shorter, brighter lens with either smaller pixels or a TC.