IMHO, if the knife is sharp (as in, the two sides meet at a single plane, without burrs) it will perform well. The need for higher grits only comes into play when you want to have a smoother slicing action. For instance, a dedicated slicing knife, like a filet knife or a Yanagi, would benefit from the higher polish more so than a clever or an all pupose chef's knife would (though the finer edge is nice on all knives, and not that hard to maintain). A 4k edge will grab the material a little better than a 1k edge, which is better than a 220 edge, but unless you are a professional chef, meat packer, lumberjack, or otherwise professional knife wielder, the difference is a matter of choice.
The bottom line is that the knife is sharp, from there it's just a luxury as to how fine you make it.