If the contract does not allow for the consumption of alcohol nor waive any of the rights and responsibilities of the property as a school, I'd say that since it is owned by the district and school IS held there, it is a school for purposes of the law.
But, the production people can certainly thumb their noses at the district. they can then hope the police are not called, and they can also hope they do not need the facility any more so that when the district tells them to get lost, they can do so without any problems.
Okay, here is the definition of a "school" per section 436.1111 in the Michigan Liquor Control Act:
(8) "School" includes buildings used for school purposes to provide instruction to children in grades kindergarten through 12, when that instruction is provided by a public, private, denominational, or parochial school, except those buildings used primarily for adult education or college extension courses. School does not include a proprietary trade or occupational school.
So, it refers to the building. By that, I would assume that if any PART of the building is used for education (and assuming it is still zoned as a school and not a subcontracted commercial space) then it meets this definition under the MI liquor laws.
However, it also seems to indicate (if I am reading it correctly) that college and adult education courses are not considered schools for this purpose.
I am NOT going to read the entire act to try and interpret whether or not a license is required based upon it being a commercial property or not ... too much reading.
Bottom line, if they really want to have the cast party with alcohol, they might put themselves at risk. They can always seek a legal opinion from an attorney, but that might not do them much good if the cops show up.