I would definitely send an email expressing interest. I'd also briefly update them on what classes you're taking, and if you anticipate you're going to do well, let them know the classes are going well.
For myself, while I was waiting for an interview for NYU, I let them know I had graduated and did not plan to retake the DAT, so couldn't provide an academic update or new scores. I used the opportunity to let them know of my travel plans prior to matriculation, my work status (to save some money as a rainy day fund + to fund my travels), and ended it by expressing how I hoped to have an opportunity to visit their campus soon. I received an email response thanking me for the update and received an interview invite a few days later.
If you don't have updated grades or scores, I think it's just as worthwhile to detail what you want to do for yourself (given your GPA and DAT aren't terribly low). You can take this as an opportunity to show them you are well-rounded and have a life outside of academia.
