Should I have a complete profile to apply for jobs or be considered for a position?

No. As a matter of fact, you can register without even uploading a CV file.  However, it is better to include everything you believe a potential employer would want to know or have.  Along with your CV, it is worthwhile uploading a recent photo.  Nowadays, some employers might also require candidates to have a video presentation where candidates briefly introduce themselves professionally in a short video clip.  The more info you provide the higher your chances of getting a call from potential employers.