It's possible theoretically, but it won't happen. Transferring theatres is a VERY expensive proposition (usually a couple of million dollars) and it's only done with big blockbuster hits that have the potential to run for years after the move (Cabaret, Chicago etc....).
Piazza is a terrific show, but it's potential audience is rather limited with its esoteric subject matter, a very complex score and no stars above the title. Despite a strong slate of reviews and tons of nominations from the OCC and Drama Desk, it's attendance numbers have been in the 50s, 60s and low 70s. No producer would invest money to move a show with box office numbers that weak.
Now, I guess if somehow it were to sweep the Tonys, including Best Musical (never happen) and immediately sell out through September, perhaps the scenario might change. But, it's highly unlikely.
"What a story........ everything but the bloodhounds snappin' at her rear end." -- Birdie
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"The Devil Be Hittin' Me" -- Whitney