If you’ve already been accepted to another program, you have nothing to fear by contacting the desired school and asking them this question. I would even suggest you call to confirm that they received your application. I applied to several programs, and asked several people to send in recommendation letters for me. Turns out, my “choice” school received one of the recommendation letters “too late” (incomplete application) and I was closed out of the following semester. I chose not to delay grad school and went elsewhere.
Call and confirm that they received your application and that it is complete. Then ask what is the interviewing process (meaning, when can you expect to hear).