The dpreview page for Nikon D4 mentions that the camera can shoot 9-11 fps. Considering 11 fps is the absolute maximum, but it can go as low as 9 fps, we can conclude that the Nikon D4 can in fact shoot at about 9 fps when capturing 14 bits/pixel. This is because the processor takes longer to write the increased amount of information to the memory (14 bits per pixel as opposed to 12 bits). However, you can push the camera's burst rate by switching to 12 bits/pixel, which will yield around 11 fps, according to dpreview.

Do bear in mind, however, that 14 bits/pixel can write values up to four times as high as 12 bits/pixel; it will mostly translate into better shadow area-quality, because the shadow pixels which generally get less exposed will have greater detail. This is simply due to the fact that the value in each pixel can vary more freely with 14 bits, hence it is able to store more accurate information.

So now there's a decision to make: better shadow quality or higher burst rate? It shall be dependent on each particular situation.

For a more detailed explanation on 14 vs. 12-bit recording, go to this explanation, which briefly describes the pros and cons of each setting over the other.