Lerner and Loewe's musical has been revised for the stage by Heidi Thomas.
The evening will celebrate the work of playwright/director Moss Hart.
Errico replaces Victoria Clark, who was previously scheduled to perform at the gala.
Recent Pippin star Tovah Feldshuh will host the event, which benefits TDF's accessibility programs.
Tony Award winner Victoria Clark will reclaim her wings at the Broadway Theatre later this month.
Manhattan Concert Productions produces the evening, to be held February 17 at Avery Fisher Hall.
Manhattan Theatre Club and MCC Theater's coproduction also stars Danny Burstein and Victoria Clark.
Take a look at Parker with costars Danny Burstein, Victoria Clark, and more in the new production.