We can make fake cheese from veggie oil. If we used oil from cheese instead, would it still be "fake" cheese?

I thought of this while inspecting some unopened cheddar packages I'd forgotten to refrigerate after getting groceries this past weekend. There really wouldn't be much problem getting enough of that oil together to make some "fake" cheese - would it work the same way as it does with veggie oil? And would it still be considered "dairy"?