When I started applying for grad schools, I knew that one of my professors was going to have issues submitting his letter on time (he has a history of this sort of thing). My top choice school had a deadline of December 23rd, and all of my emails to him went unanswered. This school came back from break today, and I woke up to a voicemail from them. I figured that they would be asking me about the missing letter, but the message turned out to be an offer of admission.
I'm a little shocked--not only did I get into my top school on the very first day they started looking through applications, but they accepted me with an incomplete application? This seems a little unusual to me, and I'm paranoid that they made a mistake. I know I had a strong application, but I don't know if it's so strong that they don't need all three letters. A friend of mine (another top student) applied and hasn't heard from them, and he has a complete application.
Is getting in with an incomplete application even a thing? And should I keep bugging my professor about submitting his letter? Does that even matter now?