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:
[cf. copy of complete show, below, including the hugs]
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 15 May 2017:
And here's a copy of the complete show, bringing back the rendition of America.