I believe both Six and On Your Feet recorded their cast albums live from a performance at the theater. I think The Woman in White did that too, although in London.
"No Time at All" from the Pippin revival was recorded with hundreds of fans volunteering to be in the chorus. I don't think it was at a Broadway theater, though, but someone here may know more. The rest of the album, I believe, was recorded in typical fashion in a studio.