Dear nk1981,
I do think you should disclose your conviction. There is usually a small text box where you will explain what your conviction is for and how that is not going to be an issue. A DUI is not a deal breaker as long as you are convincing that you don't have a drinking problem now. If you had been convicted of a violent crime, then that might be different and would probably warrant a criminal background check. Schools will also do a background check if they believe something in your application to be fraudulent, like you wrote your own recommendation letters.
I do think your story on what you learned from the DUI could make a compelling essay; just remember to focus on how you have changed and what you learned from the experience, not give details on how the DUI happened. Everyone makes mistakes when they are young--what is important is what you learned from them.
Best of luck,
Lisa