I would not expect this to influence your chances of being admitted in any direction. I think most departments just want to avoid their faculty getting spammed with applicants asking about their chances.
I always do though, irrespective of the indications of the FAQ. I think a very polite e-mail asking if the professor is planning to take grad students in the following years can not do any arm, and can help you decide whether to apply or not.
I can hardly imagine any other relevant question, for if it's about the application process, specific contact information can be found in FAQs and if it's about their research, you can always read their papers.