That's a good point actually. The way programs work are so different. Some programs, like mine, you have to express interest in who you want to work with when you apply. There has to be room in the lab and funding available. But, I forgot other programs do it differently. I hear there are some programs out there where you have a ton of advisers.
I don't think they would find out who your adviser is, unless you offer it up in the essays or a letter of recommendation comes from him/her. I'm sure plenty of applicants leave it out, because it's not always as well defined as it is in my program. No worries.