ArcObjects throws the COMException, "Cannot convert polylines or polygons with curves to JSON format" when converting a polyline or a polygon with curves into a JSON object in ArcGIS GIS Server 10.3 and later versions.
This issue is not reproducible in the current release of the software. If you are encountering this issue, please contact Esri Technical Support (for customers in the United States) or your Esri distributor (for customers outside the United States) to resolve this issue.