The cast recording was made after the production closed. The booklet for the CD issue gives the recording date as November 18, 1961, but that is incorrect. That was the final day of the Broadway run, which was a Saturday. There were two performances that day and so it's clear that the cast recording was not made that day. Variety reported that the recording was made on November 20, two days after the closing.
As with many shows of the period, it is difficult to get exact information about how many previews the show played on Broadway. It is known that there was a benefit preview for the New York City Mission Society on Wednesday evening, October 18, 1961. As the show had played its last performance in Boston on Saturday, October 14, it seems likely that the preview on October 18 was the first Broadway preview. If so, it seems likely that the show, which opened on Monday, October 23, played five previews on Broadway but we have no way to be sure at present.