The closing performance will simulcast LIVE to movie theatres from the Nederlander.
And it's neither highly likely nor unlikely that it will be recorded for DVD release. They have done this "LIVE Simulcast" stuff before with things like operas at The Met and such. Some have made their way to DVD while others have not.
Carmike Cinemas is exclusively a movie theatre company. They don't do DVDs. So a DVD production company would have to be hired seperately. The producers would make that decision.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle