The Houghton Lake and Barker City Railroad was owned by the Roscommon Lumber Company. It was a logging railroad and not a common carrier. Doubtful that a logging railroad would build a station. Some online searching of these companies will give a little more information.
Whether or not a freight car could make it from Hauptman Junction to Edna is unknown to me. That would take an intensive search of extant historical records. And if the search turns up a lack of positive evidence, that doesn't mean it never happened. It may mean it wasn't recorded or that record has been lost to time.