The maximum current you can take from a battery is generally proportional to the battery's capacity in (m)Ah. Internal resistance is the killer as you try to take more current. That will cause a voltage drop, so you get less power out than you think. Unfortunately that power is released as heat inside the battery. Too much of that is not a good thing! As a designer you would probably lean towards worst case here. You're in the middle of Africa at noon on a sunny day, with a big white lens and making use of servo AF tracking the wildlife as it moves around... in that condition, the system still needs to operate safely. Normal shooting may therefore appear to have more headroom than is given.
If you have two batteries in parallel (assume they're perfectly balanced for now), you just doubled the current you can take compared to a single battery. Or, for the same draw as a single battery, the current you take from each is halved and you gain a little efficiency.
As for driving the AF faster or not, I'd be surprised if the power wasn't regulated between battery and lens, and voltage converters can be very efficient these days. The AF speed is likely a system feature involving both body and lens, such that in use the power drain due to AF is kept in a safe region. More power available means it may be able to command faster AF. I certainly wouldn't base predictions on the assumption that the motor would be a resistive load and how that responds to varying voltage.
Anyway, the integrated grip isn't my thing anyway, and here I have to wonder if its a name game. If indeed the 70D is going upmarket, could that take over where the current 7D sits? Only then could a 1D level and spec body become more possible for a 7D successor. But still, I find calling that a 7D mk2 tough to swallow. I think that would deserve a new model number. 2D, 3D, 4D are still available, as are variations of the 1D name. I don't think it could be 8D or 9D since that would be positioned lower than 7D.
Assuming the rumoured announcement of the 70D is soon, the form the 70D takes will serve as guidance as to what may be offered in a 7D position, or 1D like position. My gut feeling is if the 70D leap-frog the 7D in spec and takes its place, then the integrated grip APS-C starts to make sense. If the 70D doesn't exceed the existing 7D, then I feel the 7D mk2 will be normal bodied.
I just can't imagine something called 7D mk2 being integrated grip, but it could exist as another name.