Specifically: If a proposal reached the commit phase and I wasn't following it but committed to it, and that proposal then made it to launch, will I get the badge or not?
What falls under the category of participated?
The badges page states:
So you have to have "followed", "committed" and been a private beta user (got the beta badge) on a site that has graduated.
I don't know whether it also needs for you to have supplied sample questions and voted on other questions during the definition phase. I haven't followed a site I didn't do this on.
There is (now) a more detailed description of the steps in a later question. It says:
For reference, it and all other badges are documented in the List of all badges with full descriptions.