Have you checked your rules and regulations regarding this? For example, at my university, you can use a professional proof-reader for limited copy editing but you have to declare it formally when you submit. The Head of School then checks all the administrative matters, forms and reads or checks over the thesis. Thus chances are your supervisor would find out before submission even if you didn't 'officially' tell them.
Personally, I would tell them. The supervisor should be checking for academic content and rigour and clarity of argument, logical flow, etc. The copy editor is just checking over things like semi-colon use in APA referencing, minor typos, formatting of tables, basic expression and that it makes some sense to the reader (or at least that is what I understand).