That's how i do my alerts for people added to groups who aren't pre-approved, but i don't see how that will tell me if a user modifies their own account.
However, you did give me an idea (this may be kind of convoluted but it's just a starting point). What if we can correlate 2 different events and make an alert from them. For every time i change my own group memberships in testing I trigger an object audit event that has some of information actually populates correctly such has Fletcher\, Ryan or Domain\rfletcher. Do you guys think that might work?