The only use for a neutral density filter, may it be colour or b&w, is gaining more freedom in choice of shutter speeds or apertures, optic-wise. Such filter acts as an accessory aperture, exposure-wise.
... well... I often use an ND filter or choose a long exposure to move the film down into reciprocity failure. The change in the distribution of tones due to reciprocity failure is hard to achieve with other methods and does have a unique look; heavy shadows and lots of separation in the mids, nice sparkly highlights. I do this often in place of N+ developments, often in conjunction with a red filter on Tri-X, which bumps up the contrast a bit too. This latter is due to the way 320TXP reacts to red light and doesn't work for other films.
I use ND filters to get really long exposures at times to "erase" the people or traffic in the shot. This falls into the category of choosing shutter speeds though.
As for increasing saturation in color films: An ND filter will do no more in this respect than reducing exposure any other way. And, if the ND filter is properly compensated for, it will not result in underexposure at all, and therefore, no increase in color saturation. For B&W films, underexposing does change the look of the final print, by eliminating shadow detail and requiring a higher contrast for printing... There's no color to increase saturation in. If this is not desirable then ND filters should be properly compensated for.
Best,
Doremus