There is simply no better lens than the 24-70 II.
... unless you try to shoot handhold with longer shutter times :-) in which case you should get familiar with PS' blur reduction filter. What I'm trying to say: For walkaround photography in verying light, IS does make sense, so there's no linear "better" or "worse".
First, AFAIK, all cameras benefit from the extra light gathering when it comes to focusing in the dark. Cameras open the lenses up to their widest settings while focusing, and if the widest setting is wider, those AF sensors see more light, which means the camera is more likely to successfully focus when shooting in low light conditions.
Correct, your af capability will also drop one stop when using f4 vs f2.8 ... so in theory, there might be situations where you could shoot with the 24-105 using 3 stops of IS, but cannot focus anymore. However, I doubt this situation will occur very often as the newer 6d/5d3 are able to af in very dim light, it might be more of an issue with older af systems like 5d2 or 60d that only focus up to +0.5LV.
Second, as I understand it, the 6D's center point has increased accuracy when used with f/2.8 and faster lenses, so there's a pretty significant benefit to the faster lens even in normal light, assuming you're using the center point.
Afaik you've got that wrong: If you're shooting with slower lenses, you most likely don't profit from the f2.8 precision as your dof is deeper, but the enhanced precision slows down the af.
Last not least, speaking of the 6d (but not opening the can of worms again) @ f2.8 the af is more precise. but also more unreliable since it isn't a cross sensor anymore just like on the 5d2. Imho that's part of the reason why Canon issued the 24-70/4 which works much better with the af system of the 6d.