Hi Erica,
So are they clicking on an "x" type close button? And you want to track that?
You can do this, but you'd want to do it through an API. Then typically the API would request a campaign called something like "Closed Form". (that will be the action you can filter on in your smart lists and measure how many people are doing this).
Is there someone on your team or someone you work with that knows about APIs?