Can't answer your oc'ing question exactly.
I'm sure plenty of people have 870's clocked to 4Ghz.
A V8 and Corsair H series coolers aren't exactly cost effective means of cooling.
The best CM air coolers are the 212+ and V6GT performance wise.
Air coolers from Noctua,Thermalright,and Prolimatech are the best and will outperform Corsair Hydro coolers.