In 'Encounter at Farpoint' Data escorts an unnamed admiral onto a shutlecraft. Was the name of this admiral ever mentioned? It looks vaguely like McCoy from The Original Series, but I can't be sure.
Yes, indeed, it was Admiral "Dr." Leonard McCoy. For backstory, please see:
On stardate 41153.7, the 137-year old Admiral Leonard McCoy inspected the USS Enterprise-D during its first mission. He commented on the great significance of the ship's name to Lieutenant Commander Data, telling Data "You treat her like a lady... and she'll always bring you home." (TNG: "Encounter at Farpoint") (src: McCoy@MemoryAlpha)
The "Encounter at Farpoint" novel described it quite nicely. In his post-Enterprise days McCoy was promoted to admiral and served as head of Starfleet Medical Services. In other words he had a lot of pull even after retiring. At age 137 he learned that the new flagship would be name "Enterprise" and vowed to board it before its first mission. However, he was unable to attend the formal launch along with the other dignitaries because he had fallen and broken his hip. By the time he had mended the ship had launched. So he called in old favors, pulled strings and used all of his influence as a former admiral as well as one of Starfleet's most iconic and heroic figures to arrange a tour for himself. So the "inspection" was not an official one but rather a courtesy tour that the Admiralty granted McCoy in view of his life of service to the Federation.
You're right it is indeed DeForest Kelley from TOS. Wikipedia:
The episode features a cameo appearance by DeForest Kelley as Admiral Leonard McCoy.