Most shows that were directed by the late Gower Champion did not have overtures. He hated them because the audience frequently talked right through them--something verified many years ago while the two blu haired ladies in front of me during Linda Lavin's GYPSY chatted away while the orchestra played that thrilling overture. When I "shhh'ed" them, one responded, "It's only music."
Anyhow, the original production of TWHM did not have an overture. It was added when Pearl Bailey revived the show in 1975.
I DO! I DO! doesn't have an overture
CARNIVAL! lacks an overture, but has one of the most effective openings in musical theater.
The original BYE BYE BIRDIE had an overture, but it was an underscoring to a slide show of 60's teens.
THE HAPPY TIME lacked an overture, but started with the title tune--and another slide show.
IRENE had an overture that was "acted out".
ROCKABYE HAMLET lacked an overture, but started with the wedding of Gertrude and Claudius (the whole show was a messs).
Yes, MACK AND MABEL had an overture.
Did the original 42ND STREET have an overture or did it just start with that very effective opening number?
"Long live God!" (GODSPELL)