If it's a private school. Yes, it can.

But a public school (read: relies on government funding) is legislatively prohibited from owning a business that may lead to an exploitation of students.

However a course like this will have no problem being run to a private or public school as part of the curriculum. A lot of schools teach something similar in a "Small Business" class where students are to go start a business and the success of the business is their grade. The problem begins if you try to make it extra-curricular. In short, the school will likely not allow it.