Yes you can.
I have used Fancy Box to submit forms. It's works fine! I developed this site a few months back (http://ienablenextgen.com/bioinformatician) and if you click on the "Request Information" button, you'll see it in action. Please don't submit useless data. Thanks.
A very easy solution is to build the form on the page, and hide it will CSS. Then allow your jQuery to call the hidden form, you'll need to give the link the following attributes:
<a id="inline" href="#data">This shows content of element who has id="data"</a>
Where #data is the ID of the hidden form.
You can also call it other ways, look at the advanced options on their website http://fancybox.net/api