Is the flash output "greatly" reduced or is it "proportionately" reduced?
Instead of looking at the generalities, let's look at specifics.
What the FP does, basically, is that it fires a bunch of "short", low powered high duration flashes instead of one big hard "long" flash. Not only is the total amount of energy used by each flash much smaller, it is also "undocumented" by Nikon, so we don't know what an SB-800's actual guide number is when shot at 200 ISO at 1/2000th of a second.
However, to make this system work, it has to provide nearly the same amount of light for all of the flashes in the series. It must use the same ISO.
Therefore, each of these flashes MUST have greatly reduced power limiting the range... the higher the shutter speed, the less flashes, the less range.
I have found in using my D80 that the range of an SB-600 at 1/500th of a second has about one third of the range that it has at 1/200th of a second (full flash). With the D40, it has full-range at 1/500th.
So, if I can properly illuminate something at 100 feet with the SB-600 at 1/200th, I can only illuminate it properly at about 40 feet in FP mode.
I don't know if that qualifies as "proportionally" but to me it makes the mode of very limited use, since I shoot a LOT of stuff in the 80-100 foot range.
If you shoot up close on targets that are not moving, it really doesn't matter that much. If you shoot longer distances, it is the difference between being usable and not.