This can lower your chances or eliminate you from being selected. Follow the directions given for the scholarship you are applying. A generic statement written for all applications will not work well. Scholarship committees really read these statements and partially base their decisions on what they read. Be sure your statement addresses the suggested topic.
Personal letters are much more effective.
Allow plenty of time. Don't ask for a letter of reference too close to your scholarship deadline. Different scholarships may request different types of references. Some will only accept references from professors while others may accept many types of references. In most cases they will never meet you in person.