Coderunner so far no opportunity to try but my gut says easily yes. I was getting BIF with the a7Rii + LAEA3 + 70-400gii and it has the same limitations (no zone, only Center, AF-C best, and so on). Acquisition of still shots at different distances is way way better than with the A7Rii via Metabones T iv with any EOS lens (and I tried 300/2.8 IS II, 400DOii, and 500ISii. BUT I will say this, in an area where you have widen open spaces where you can see the target/bird coming from some distance, you'll have better odds.
So based on actually getting BIF with the mush slower A7Rii I say adapted EOS lenses and the a6300 are very doable, the a6300's AF system is just so much better AND as you've read no EVF refresh rate problems.
I've also shot BIF with the a6300 + FE 70-200g and it's like cheating. Check out this one-
https://www.flickr.com …6421267592/in/dateposted/
I got around 300 hundred shots that day all looking just like this one machine gunning with the a6300.....problem as you'll easily see is lack of focal length.
If Sony would give us a 400mm then they could rock the wildlife/BIF world, on a native e-mount lens the lock-on and tracking is amazing.
We have the FE 70-300 on pre-order, the extra 100mm will help some.
Tomorrow we hope (weather depending) to take Oscar out to a field where we know hawks are nesting. Oscar is a life-size plastic Great Horned Owl which we have adorned with added real feathers...the Red-tails in my area hate GHOs, so we'll see if they swoop him. If so I'll be waiting in a blind....