K.M.
I worked for an independent school for 5 years with over 100 employees and about 500 students. It was an old well-established school in New York City and it did not have a dedicated HR person. It did have a business manager who took care of many of the HR tasks but all resumes were filtered through the head's office.
Sorry, that is not much help. I don't think it is a bad idea but if you can mix it with other business functions for a business manager type position then you might be more likely to convince them.