First off congrats!! I don't think telling the other school about this will cause any movement as you can stay on the waitlist there still after- unless you need to CTE to the school you just got accepted to in a week. If that's the case you can say something. If anything you can send a letter of intent to the school you're still waitlisted at. I say this because I know NYUs dean of admission said LOIs will only do anything if you are CTE or PTE at another school. Which makes sense to me b/c if they now will see that you have an acceptance at another school this LOI tells them that you still really want to go to their school.
Regardless I don't think anything like this will really cause much WL movement, but I know I would def feel better doing everything I can.