Could I use chicken stock for the sauce or polenta?

I agree with Dinner. It's a wonderfully bright, fresh dish the way it is. I love cooking with stock, but once in a while, there's a dish that's better the way it's written.

I also really like this dish, and wouldn't recommend adding broth -- I think its fresh, bright flavors might be dulled a bit by broth.

Sure. It doesn't 'need' it in terms of adding flavor (it's a really delicious dish as is) but if I don't think it would hurt either. I think the flavor difference with broth would be much more subtle in the sauce than in the polenta.