Snopes says no.
I hadn’t heard this one before — too busy with the old ham sandwich rumor, I guess.
The story goes that Mama Cass ached to join the Mamas and the Papas but John Phillips wouldn’t let her in because she couldn’t sing the high notes their songs required. Then in 1965, Cass was hit on the head by a falling pipe, and when she recovered from the concussion she was miraculously able to sing the notes. She joined the group and the rest is history.
Snopes admits that Mama Cass did make the claim, repeatedly. But they disbelieve it. It was a cover story, they say: John Phillips wouldn’t let Cass into the Mamas and the Papas because she was “too fat.”
After he finally did let her in, and she was a huge hit, neither Phillips or Cass wanted to tell fans the real story. So they invented the head-bonk miracle instead.
Here’s Cass telling the story in a 1968 interview with Rolling Stone. (Her take: “It’s true. Honest to God.”)
On the whole, the ham sandwich tale was simpler.