The only way to have Ray Charles appear in a show's finale was to let him sing. It happened as the last sequence of this show.
A contemporary edition of The Utica Observer revealed the official title (Kraft Salutes the 25th Anniversary Of The Country Music Association) and names most of the 33 artists who contributed to the show (and this finale). Don't miss Willie Nelson's look when he observes how Reagan hugs Ray:
America The Beautiful:
[Clip was removed from YouTube]
The Utica Observer also described how Ray performed together with Ronnie Milsap. "The spontaneous and prolonged standing ovation, which includes President and Mrs. Reagan and Vice President and Mrs. Bush, rocks Constitution Hall."
Medly of Don Gibson tunes, with Ronnie Milsap - Oh Lonesome Me, (I'd Be) A Legend In My Time, I Can't Stop Loving You (+ final shots with Ray and Raegan shaking hands):
Update 19 February 2017:
This clip emerged on YouTube. Ray & Ronnie sound better here (but look radically different), doing a medley-duet on Your Cheating Heart and Hey, Good Lookin'.