We’re told that the larger battery seen in the EOS-1D X is part of the reason it will autofocus bigger lenses better than a camera with say an LP-E6.
Which means using 2xLP-E6 in the grip should allow the same autofocus performance, and, I would add, should also allow driving a burst speed of 12+ fps, a feature which would draw even more current than a big lens AF.
No, dual LP-E6 ≠ one LP-E4N. With two batteries in a grip, the voltage output of them is not added, they are used in an alternating sequence. The 1-series bodies drive lens AF motors faster because the battery delivers a higher voltage.
It should have nothing to do with the fps, either - adding a grip to a dSLR isn't required for higher frame rate AFAIK (although it was with film bodies to drive the film winder faster). Even with Nikon bodies where the grip provides a higher frame rate, there's a firmware hack that enables that higher frame rate without the grip, i.e. the higher frame rate with grip is a Nikon marketing ploy to sell an expensive accessory.
Neuro, I'm not mentioning voltage at all, instead I said 'current'. I think the two batteries in the grip are not 'used' in an alternate sequence, they are used simultaneously. Actually, inserting two discharged batteries, both incapable of even letting you switch the camera 'on' when used alone, will let you switch the camera 'on' and even shoot photos. It's the shutter count per battery that is calculated in an alternate sequence, being not possible to show 1/2 increments per battery, which would be nonsense. They are connected in parallel, so the voltage is the same, but are capable of delivering double the current of a single battery, i.e. 3200 mA instead of 1600. Moreover, the voltage used by the camera components is neither 11.1 V nor 7.2 V. The voltage is adjusted to 3.3, 5, 12 or higher, or whatever the electronics need, prior to be 'feeded' to circuits, sensor, motors etc. It's a matter of power (Watts), which is the product of electrical potential difference (Volts) x electric current (Ampere). You can feed the inverter with whichever V x A combinations (within certain limits) and, provided the input power is enough, the camera will work.
Actually, when 'speccing' a battery, the nominal voltage indicated usually corresponds to the voltage of the fully charged battery. During use, the voltage drops until it reaches a minimum that doesn't allow the inverter to produce enough power to drive the camera. If we measure the voltage of, say, a LP-E6 with 30% power remaining, the voltage is no longer 7.2V, but much lower. Nevertheless, the camera still works.
The higher frame rate with grip is NOT a Nikon marketing ploy to sell an expensive accessory, it's a safety measure which prevents the battery from overheating and the camera from running at a performance below the specs. There's a hack, but it's not totally safe: a sub-perfect Li-ion battery may explode. Sure, it's not probable, but it's not impossible, either. The hack works as long as the battery charge holds, then bye bye. It is what it is, a hack.
To summarize, I'm still convinced that a single LP-E6 batt can't drive a big white AF + IS and simultaneously drive a 12+ fps burst, but two of them would, indeed.