Employers do not like taking on people whose qualifications exceed the level of job requirements and salary offered. They believe that over-qualification can be as bad as under qualification.
Your approach would be better along the lines of": "I am prepared to take a drop in salary as the opportunities for learning offered by this position are so exceptional."
A head-hunter is technically an agent who seeks out particular potential high level employees to fit into a specific position. You seem to be dealing with an employment agency, which is somewhat different.
Student or Learner