If I understand correctly what your question is, it shouldn't be a problem. Since your JavaScript - which you are testing - is publicly accessible, the tests shouldn't do any harm. They cannot do anythin, what the users couldn't do anyways.
What can be a problem: if you produce sample data during running the tests, you are going to produce a lot of trash data in your production environment. But you shouldn't do it anyway - just mock AJAX calls and so on.