If my data doesn have any projection information stored with it, how will ArcMap handle it?
ArcMap will use that data in two ways. First, if ArcMap can sense that the data is in geographic decimal degree coordinates, ArcMap will project it from decimal degrees to the display projection. Second, if the coordinate system is not specified, ArcMap will use this data in a limited fashion. If it is the only coordinate system used in the map, it will work just fine. If you set a coordinate system for the data frame, you will probably not see your data because ArcMap will not have enough information to perform the on-the-fly transformation. If you add data that contains projection information, ArcMap will give that data precedence in defining the coordinate system foe the data frame, and you will be unable to see the data whose coordinate system is not defined.