I don't think it is a good idea for many of the above reasons mentioned here.
As someone said keep the 2 things seperate. I would use this handy man when I thought he could do the job expertley/ paying him a competive amount of money per job
When the job seems too complex for his level of experience I would go elsewhere for that help. I would always consider using him first. He would also be very convient because he would be living at the property. It would speed up tenant repairs and he would be close enough when you thought he should improve the repair. I would also want to keep him as a permanent tenant. I would use him when it was good for me to use him at a rate negotiated with him.
Your rent for this apartment is $500. Do you have $500 worth of labor for repairs a month? That seems rather high for only the labor. What is your total rent roll?
This could be a win win situation for both of you. You would steer most of your work and repairs to him and that should make him happy and you would have a handy man on site and that would make you happy and give fast attention to your tenants You would also have a permanent tenant that would not move because he had a job by remaining as a tenant. Be good to him and hopefully he will work out well for you