Does VR work while recording video or using Live View?

Yes, it does. Some of the confusion comes from Nikon itself, which very early on in the history of VR posted a support response that VR requires the shutter release to be half pressed to operate. This was in response to a question about when focus is set to be enabled only by the AF-ON button, VR wasn't active while focusing (you'd have to press the AF-ON button and half-press the shutter release simultaneously). 

Many people remember that short answer ("shutter release activates VR), unfortunately, and it was broadcast by others after Nikon made it. But the answer needs to be modified for cameras with Live View and Movie mode: both a half press of the shutter release and use of Live View enable VR; VR is also active when you record movies (as it's an extension of the Live View capabilities). 

Curiously, Nikon has gone back and made VR active with AF-ON pressed on the latest cameras (starting with the D4 and D800). Personally, it doesn't bother me—I long ago mastered the two finger dexterity necessary to use AF-ON with VR—but it does bother some, and it seems an odd omission, as the focus system benefits from a stabilized image.

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