[BradS]

Can a multicoated filter actually improve the image quality of an older lens that has few coatings, if any, or coatings damaged or worn away by years of cleaning?

Without going into the physics of why...the simple answer is NO.

Think of it this way, adding a filter adds two more surfaces of glass....which increase flare. The multicoated filter would only increase flare by a smaller amount but it would still be an increase.

You may want to try using a good lens hood with those older lenses.