Is it necessary to have data stored in ArcGIS Online to use collector and have the data sync when back in coverage?
No, you don't have to. From Take maps offline—Collector for ArcGIS | ArcGIS the data requirement is that "All feature layers in the map are sync-enabled. These can be hosted feature layers or ArcGIS 10.2.2 Server or later feature services. " You then also need a supported base map.