You could make a replay that triggers parameter changes for the breath behavior, but I think you'll find the timing is weird because the breathe behavior wouldn't start breathing at the trigger, it would just pick up at the point in its oscillation that it was at when you pressed the trigger.
But the breathe behavior is really just a transform on a handle, which you can do with a Transform handle and behavior. Combine a recording of that Transform handle's Scale parameter with a Face behavior performance (so the head moves up and down with the sigh), and a LipSync track so the mouth moves with it and you could probably make something that'll look better than what triggering the Breathe behavior would do on its own.
DT