No information on a "Gates School" near O'Kean,.The schools in the area from the early 1920's were the O'kean School, the Connelly School and the Haney school.The O'Kean and Connelly school were well established in 1921 when the students were photographed and identified by name.
The Haney school was in place but not opened [or re-opened] until about 1944-45 and closed again for consolidation in the later part of the 1940's,when about ten area small schools were combined in to the Delaplaine school, to which school busses were used for transportation. Delaplaine is about the center of the Jones Township, in Greene County.
I know there is a photograph published on the "Gates homeplace", [formerly the "Green School"] with identification of the people on the long porch. If you are looking for any Gates you will have to look at the 1921 photo of the Connelly school.
There was a large log house in O'Kean during WW2.Know as the "Legion Hall" it was used during the war as a place to make Mattresses.The American Legion was not established until after WW1, What the building was used for prior the them,I do not know.
If you have any of the Gates, first name I can check them against the photographs I have, which were published in a book.