The ArcIMS ArcMap Server must be used as a Virtual Server. True curves are not supported by the Image or Feature Virtual Server.
If true curves are present in a geodatabase, they are displayed and act like true curves as long as ArcGIS clients are used. True curves are not seen if ArcGIS clients are not used. If an image or feature service in ArcIMS is used to publish the data instead of an ArcMap image service, true curves are not displayed in the data.
This is due to the geodatabase storing two representations of the curve segments. One representation is the true curve that can be seen by ArcGIS clients, and the other is the multiple segment view, that is displayed with non-ArcGIS clients.