I applied several times before I turned 18 and heard nothing. Once I turned 18 I got a response very quickly (probably within a week or so of submitting the application). The response was an offer to set up an in-person interview. During the interview they asked basic questions (why do you want to work here, what is your favourite part of the park, etc.). They were very nice and encouraging. I had worked in retail before and the interviewer gave me a choice of staying with retail or moving to a different job; I chose to switch to food service (it didn't really matter what position you applied for). She checked the available positions and offered me a job in the Wizarding World, which I mentioned was my favourite part of the park. A very pleasant interview experience, both quick and friendly.
NOTE: If you are trying to get a job there for the summer, you should apply a maximum of two weeks before you want to start. Any more than that and they will be frustrated because they want you to start immediately after your are hired, and the application process takes well under two weeks. This is both from personal experience and from HR advice (I asked HR before I applied). Good luck!