For all practical purposes, I think the answer is "no, nothing is too fine of a grit for finishing." But it also depends upon what you expect the final finish to look like.
If we think about what we're doing with sanding, we can rationalize our way through this process. The surface of wood is an uneven surface with repeating ridges representing the grain.
And when we sand, we're knocking down those ridges. The finer the grit of sandpaper we use, the smaller the ridges become.
We have to move to ever finer grits of sandpaper while we're sanding otherwise we're just changing around the ridge pattern on the surface of the material. That becomes obvious when we look at sandpaper under a microscope.
600 grit sandpaper under high magnification
Sanding is just carving out smaller grooves in the wood, with the depth of the groove being defined by the grit of the sandpaper. Moving to really high grits (like the 2000 you mentioned) merely continues that pattern of decreasing the height between the various ridges on the wood. The net effect is that the material feels more and more smooth.
There is a possibility that using too high of a grit would impede the stain from being absorbed by the underlying grain. Regardless of the stain and pigments potentially being impeded in their absorption, smaller ridges from finer sanding will reflect light differently causing the more finely sanded piece to appear different from the less finely sanded piece.
Keep in mind that when the wood absorbs the stain it will lift the grain, undoing the some of the work that you had put into the finish.
It's also worth noting that some finishes that end up looking like smooth glass require wet sanding with progressive layers of sandpaper all the way up into the 1500 or higher realm.
Finer grained woods are less likely to show as dramatic of a difference with higher levels of sanding. This would be due to the woodgrain already being tighter and the separating ridges being smaller.