Why bother to send your resume to an employment agency?

Will a recruiter ever act as your agent who will help you find your next job?

The short answer is: NO. 

An employment agency is paid a fee by the hiring company; to applicants, service is completely free of charge.
Finding a new job remains the responsibility of the candidate. Recruiters however will be highly interested in you when they have an assignment from a company to fill an open position.
Therefore, it pays to send it your CV to an employment agency. They will always search in their database.