The new musical comedy comes from Amber Ruffin, David A. Schmoll, and Kevin Sciretta.
Theatrical non-profit Broadway Cares will receive the Marion Dougherty New York Apple Award at the February ceremony.
Judd Apatow and Michael Bonfiglio's film, Mel Brooks: The 99 Year Old Man!, premieres later this month.
The institution is the ten-time Tony honoree's alma mater.
Al-Kadhi is the author of Life as a Unicorn, which received both the Polari First Book Prize and a Somerset Maugham Award.
Michael Herwitz will direct David J. Glass' new play.
Ellie Heyman will direct the new musical from Will Van Dyke and Jeff Talbott at Utah's Pioneer.
The play is currently making a long-awaited Broadway debut via Manhattan Theatre Club, with Carrie Coon and Namir Smallwood starring.
The one-night-only concert will be the first to utilize Radio City Music Hall's new Sphere Immersive Sound System.