Cecil’s answer doesn’t go far enough - I am pretty sure that “Elvis has left the building” didn’t become a popular catchphrase until David Letterman asked Al Michaels to use it as his home run call. Before that it was only used in the literal sense, i.e. to mean that Elvis Presley has actually left some building.
Looking around on google, there are references to Letterman using “Elvis has left the building” as a catchphrase, though I didn’t see anything specifically related to your ancedote.
It’s pretty hard to cite a talkshow appearance :). What I do remember, though, is that is was when Letterman was still on NBC, and Michaels was broadcasting the World Series. I think that makes it likely that a New York team was in the series that year, but not necessarily.
Letterman suggested a list of homerun calls that his writers had made up. I don’t remember the others, but he urged Michaels to use the Elvis one.
Michaels didn’t use the call, but he did say (after a homerun) something like “David Letterman told me to say ‘Elvis is out of the stadium or something’”. He didn’t remember it right.
Anyway, it was after all that that it started to pop up as a catchphrase. [uh, I’m pretty sure]