I'm curious what the purpose of the Kano is? If you plan on firing the next shot right away, is having a light coating of rust preventative in the barrel helping anything?
MSU, I feel that the kroil will act as a bit of a lubricant for the barrel kind of like oil in a piston cylinder. A cylinder is honed with a cross hatch pattern to hold some oil to lubricate the rings as they move. The kroil applied and then wiped with a dry patch will leave a lite film in the micro finish of the lapped barrel. This may or may not lessen the fouling during break-in, or help with the burnishing, but it sure can't hurt. If I assume that the carbon that collects in the "Valleys" of the microfinish actually preform a vital function, then I can surmise that a bit of kroil in those valleys may be benifital, until that carbon arrives. Can I prove it? No.
Most barrel makers are lapping with a abrasive grit of 100-150, this abrasive brakes down a bit as they lap, but the results of the lapping is a deffinate texture to the steel that will hold lubricant like a cylinder wall.
This kinda explains why I feel a 800-1200 grit bore polish is a bad thing, more surface contact with the bullet increased friction and pressure, and copper that galls or smears down the bore.