I was complete for MSTP in August, and my stats are below. I emailed them a letter of continued interest in December, where I reiterated my interest specifically in their program in ~700 words. I did not have any significant updates, only that I had continued my research position since August. I received an II a month later in January. In my opinion, the letter of interest can only help! You get to show your specific interest in the school, and if they unfortunately choose to reject you, at least you expedite the process. I think you should go for it. Good luck!