Should students with learning differences contact the admissions office during the application process? Before applying? After applying?
This depends on your personal situation. There is no requirement that a student disclose their learning differences, and colleges cannot discriminate against applicants based on their unique learning needs. If it might be helpful to the school to know about your LD when evaluating your application, it could be appropriate to inform them. If not, there is no need to disclose.
Students with LD who have questions about a school's services or how to receive services should contact the DSS or Disability Support Services at the college. They will be able to answer all of your questions. If you are not planning to disclose your status to admissions, don't be too concerned that DSS will somehow flag your application or otherwise let admissions know that you are seeking services. The two offices typically operate very separately from one another.
Once you've been accepted to a college, it's a good idea to register for the services you are entitled to even if you don't think you'll use them. The first semester of college will be a period of major transition, and you may find that the help you didn't really need in high school is definitely required at the college level. You'll save yourself time and energy if you're already set up to receive services and can begin taking advantage of them as soon as you recognize the need.