I've always been suspicious of Gulen-backed schools, as they appear to function as a giant money laundering scheme for Gulen himself. They are under investigation by the FBI for their financial practices, and Gulen schools were shut down in some states for financial mismanagement, including spending large amounts of money on airfare/lodging to bring Gulen supporters over from Turkey to act as "teachers."
Basically, I wouldn't worry about the fact that the leader/movement is Islamist but I would worry quite a bit about the financial mismanagement and the fact that the whole scheme seems more about laundering money than education.