No they never did as the run was too short to permit such an expense. The length of the run had nothing to do with it. Shows with much shorter runs have been recorded. Personally, I quite liked a lot of the production, particularly the performances of Lauper, Jim Dale, and Nellie McKay, whom I thought was divine. Wallace Shawn's translation had many head-scratching moments ("A guy can crush all men / beneath his heel / Say I'm a butcher / Others are just veal," anyone?), Cumming seemed ill-at-ease, and the way they handled making Mac and Brown's relationship overtly homoerotic was often laughable, but a lot of the individual performances and a few great staging moments made up for it. Definitely look on YouTube and judge for yourself.
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body