For the most part, no. Whether you list a university or a specific program as first, second, third or higher on the application is not normally a factor in the universities’ admission decisions. A university must make its policy clear in its own information where there are exceptions to the policy of using the numbered list of choices.
Your numbered list of choices does provide valuable information to the university admission offices. This is particularly true for limited enrollment programs. Admission officials use this data to project the number of applicants who are likely to accept offers of admission, so the university can plan its resources accordingly.