I shoot with a friend who has that combo (among many others) - the A7RIII and 200-600mm and 100-400mm - he gets very nice results with them and feels it's a very good combo. If you search around on Dpreview forums in the Sony full-frame board, look for rgwaller. Here's a thread with some of his samples with the A7RIII (I think mostly with the 100-400mm in this post):
A7R3 great for wildlife photography: Sony Alpha Full Frame E-mount Talk Forum: Digital Photography Review
He has a lot of gear - he also has the A7Riv, A9, and new A1. He put a lot of miles on the A7rIII with wildlife - a few hundred thousand shutter actuations...and was very happy with it.
I use the 200-600mm on the APS-C sensor A6600, and love the combo. I also shoot with the FE 100-400mm GM lens, and I use the 1.4x teleconverter on the 200-600mm when I really need the reach. The Sony bodies are quite capable with focus and resolution in low light, even APS-C...I shoot in dark forested areas with small warblers passing through on migration where I have to push to ISO 6400 and handhold shutter speeds under the 1-over-focal rule, and shoot birds-in-flight at dusk with very low contrast, and focus is still instant and reliable and image quality quite solid with good detail, low noise, and good color retention. Some lower light examples with the A6600 and FE 200-600mm below
Pine warbler, F6.3, 600mm, ISO 2,500, 1/500 shutter:
Grey catbird, F6.3, 338mm, ISO 6,400, 1/200 shutter:
Whip-poor-will deep under forest cover, F6.3, 600mm, ISO 3,200, 1/200 shutter:
Male painted bunting, F6.3, 506mm, ISO 3,200, 1/500 shutter: