There's no way to do this in Ch now, but I've added your request to our feature backlog.
Inside AE proper, you can do this using Convert Audio to Keyframes and drive the Y position of a jaw layer. See Adobe After Effects CS6 - Converting Audio to keyframes (Tutorial by VOXLAB) - YouTube for an example (though that one uses scale).
Can I second this feature request? It's cool that Nutcracker Jaw can actually watch my mouth, but I think a lot of us would prefer it be driven by sound. I'm having a hard time trying to open my mouth wide even for words where my mouth doesn't naturally open!
But I do want to mention how much I'm enjoying this tool - although no amount of reminders is going to stop me from hitting command-S.
On the contrary! I find the Nutcracker Behaviour as is now very good! I would and will post a feature request that will talk about the possibility to increase mouth shape control I think gives the best results and there's lots of potential there still encumbered.
I CAN speak softly with an very open mouth but I can not shout with my lips closed… That's one reason why I would challenge for the nutcracker to stay tuned to video, not audio.