If you can find a job that is appropriate for him, than why not? It may be a great way fro him to learn about work ethic, be in a positive environment, learn some new skills, and become more responsible. Do you think he would be able to maintain the attention span and be held accountable for tasks? It will have to be the right job, something low stress and easy going, but it could be a great opportunity. Maybe even something within the family could be nice. Do you have any relatives that need cleaning or simple yardwork done? He doesn't have to get a part time job that is from a local business, it could just be a family project.
This may be a great opportunity for your 11 year old, just make sure it is the right job for him!