Unfortunately Bryan I don't think so! AFTER MIDNIGHT does have a few live tracks on their YouTube page I believe.
"Oh look at the time, three more intelligent plays just closed and THE ADDAMS FAMILY made another million dollars" -Jackie Hoffman, Broadway.com Audience Awards
Yes. In the olden days it was common for shows to advertise "Original Cast Recording on [name of label]" in their posters and newspaper ads for months before the shows arrived. Recording sessions were scheduled, generally, for days within an opening, and (get this!) the OCRs would be in stores in a matter of days!
The only one I recall from recent memory was the Chorus Line revival, since they recorded their OBRCR during their preview run in SF up at Skywalker Ranch, so that they could have it ready for opening night. But obviously they weren't wondering whether to cut/change any songs like a new show.