I found a gallery of programs for Shipstad & Johnson's Ice Follies from the 1940s-70s, with cover thumbnails and summaries of the respective shows. The collection reflects all the years Batman was on the air.
The absence of Batman on a program cover or in the summary descriptions makes me doubt the Batman revue was part of the Ice Follies. I suppose it's possible the owner of the site just chose not to include the Batman show in a summary, but given the popularity of the TV show (and, presumably, the cost of licensing the characters and costumes), it seems likely the show would've been featured on a program cover, as Snoopy was in 1972.
I hate it when I remember something but cannot find anything to prove it. Now I have just a tease and that really gets me.