Well, that was more than 2 years into the run. They must have added it in at some point.
According to Suskin's orchestration book, Champion cut the original overture during previews (which reflects the note in the score that says "The Original Broadway Production performed without an Overture"). He also says that when they wrote an overture for Pearl Bailey, that "Champion wasn't around to object." So, I assume the inclusion of the recorded version (which, btw, is not the actual original overture that was written and included in the published score) was done without Champion's assent as well.