I would recommend against doing this, to be honest. In my opinion, every application material you submit should provide the reviewing committee with more information about you as a filmmaker. The more data points you can produce that show how creative you are, and prove that you know how to tell a story, the better. Plus, using a different writing sample can allow you to correct for any insecurities you have about the rest of your application material. For example, I felt insecure that my video option came across a tad juvenile, so, in my project questions, I really laid it on thick about how structured/organized I am, with a very professional format and tone.
In a nutshell, your application portfolio is exactly that—a portfolio. And the common wisdom for any successful portfolio is: diversify!