While it's not unheard of for a production to swoop in and take a theatre this quickly, I've only heard it being feasible in a subscription house with built-in ticket buyers (See 2010 - "Lips Together, Teeth Apart" yielding to "Everyday Rapture"
There is no way, even if announced tomorrow, a full-scale show could swoop in quickly enough to generate ticket sales and get its act together. The only feasibility would be if Barbara Cook's show took the Booth.
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