If the app is intuitive enough that when I land on the page I immediately know what it is, what it does, and how to use it, I'd say go for it. But if I land on your page and see and app that I don't immediately "get" I'd bounce pretty quick.

What might be kind of cool is have the landing page be the product demo like you had said, except with a modal window similar to twitter bootstrap's modal plugin that gives a quick paragraph or two of what the product is and how to use it.