Got my 70-200 f2.8II back from my friend. I did some low-light testing around the house. When methodically testing, AF performance is consistent with the 24-70 f2.8II. DSLR-like in good light. In low light, unreliable with AF-S selectable point small, but very much useable with a medium AF area, and even more so with a large area. That was when doing AF testing on random objects around the house.
When I did some 'live' shooting of the kiddos I made an interesting discovery: face detect works with adapted lenses! AF works considerably better when the AF system 'finds' a face within the AF area and focuses on that. This makes me feel much more confident in the ability to use the a7rII as an event shooter with adapted lenses...particularly because the face detect system works in continuous autofocus mode. If face detect works as well as it does with native lenses, the a7rII should have an advantage over DSLR in terms of accuracy when shooting people.
Also, as others have mentioned, the a7rII struggles obtaining initial focus if the lens starts off extremely defocused. Bigger issue with longer focal lengths. Definitely make use of the focus limiter, but also, it really does help to manually pre-focus on your subject before engaging the AF. Once the lens has focused generally around the focal plane of your subject, subsequent shots AF very quickly. This is very much akin to using AF on the horridly slow EF 85L where I often had to manually pre-focus the lens too. Obviously a terrible solution for sports where you're moving all over the focal plane, but not too big of a deal for anything outside of that...especially if you've used the A7 system for a while and have gotten the hang of full-on MF.
Sample shot taken indoors at night at ISO 12,800. Nothing spectacular, but a testament to the ability to AF on a non-static subject in low light:

IMAGE LINK: https://flic.kr/p/w7GD2x
DSC06716
by
Carlo Alcala
, on Flickr