High-precision processing is a must for certain applications. For example, any sort of texture addressing must be done at at least 24-bit accuracy (for FP) for proper texturing (nVidia claims that 32-bit is required, but I'm not certain their claim has much application to games).
I would tend to expect, however, that the vast majority of color operations will not benefit from any higher than 16-bit FP accuracy. However, it will all depend on the situation.
But I will say that there will be a marked difference between 16-bit FP and 12-bit integer (despite the fact that they each have the same accuracy, 16-bit FP has a higher dynamic range, meaning it can properly calculate darker and brighter colors). There is a simple situation where 12-bit int falls far short of all of the FP color formats: specular lighting. If you want shiny surfaces to look right, they'd better be calculated in floating-point color.
Regardless, these aren't the old days of 16-bit vs. 32-bit color. Back then it was obvious: when too little color depth was available, there was dithering or banding. Today, just because of the fact that so many other types of values can be stored and calculated in the video card, the differences won't be so cut and dry. The exact nature of the differences will be different depending on the shader, and, therefore, won't always be as easy to spot (it's easy to see the differences if you know what to look for).
Update:
One last thing. I still think nVidia was doing the right thing about including different precisions in their NV3x line. However, their implementations definitely do have their flaws. Fortunately, the primary flaw (lots of 12-bit int calcs required for optimal performance) appears to have been solved for the NV35 (and presumably higher) chips.
By offering multiple precisions, game developers won't need to use the highest precision all the time. They can drop down to lower precisions for dramatic performance improvements when the extra precision isn't needed (and, I believe, it often will not be needed).