No, AF won't be as good at all and there is no peak filter.
What makes you say this? Do you actually have the adapter and FX/DX lenses? I have, and according to my tests the V1 is as fast as the D300s and the possibly even the D800 with the same lens and under identical conditions. It is also extremely accurate. OK, only the center AF area works, but that's the only real limitation when modern lenses are used. Admittedly, I don't have the V2 and that 70-200/4 lens, but I have the V1 and the 50/1.4G, 60/2.8G micro, 105/2.8GVR micro, 24-120/4, 70-300GVR and had even the 35/1.8GDX and the 16-85GDX lenses together with the D300s, now I have the D800. I don't expect the V2 and that 70-200/4 to be any worse than my lenses concerning the AF with the adapter, and I don't expect the V2 to be worse than the V1 in this respect.
What's your experience with the system?