How can Kodak Color Control Patches help correct color when digitizing photos?

Those patches are used for printer/press calibration. The grey scale is used to control the exposure, contrast and dot bleed of the separations (each of the greys should be visible and distinct; the white should be paper-white and the black should be solid) and the colour patches should result in each plate showing only the colours it's supposed to show. The magenta plate, for instance, should show a "black" value for the magenta, red and blue patches with little or no density on the cyan, green or yellow patches, while the yellow should show "black" on the yellow, red and green patches with nothing in the cyan, magenta or blue areas. (It won't be perfect in this case because the Kodak cards are in really, really rough shape.)

You can use the same patches to create a custom colour profile for the image on your own printer if you have a hardware calibration tool like Xrite's ColorMunki. Or you can eyeball the patches on test prints while making colour adjustments to the image onscreen using your own copy of the Kodak cards for comparison.

The point is that the colour patches aren't there for restoration, they're there for print fidelity. You can sort of use them for restoration of old prints, but only if the colour patches are part of the original picture and are not hidden under mattes or frames -- the colour patches would need to have faded and stained to the same degree as the rest of the picture.