Hi Martin,
Geoprocessing CAN actually be performed on image service.
There are two ways to use Image services as input in a spatial analysis tool.
1. The spatial analysis tools are accepting the image service layer input, if you add the image service to ArcMap table of contents, the image service layer will automatically appear in the tool's input drop-down list.
2. If you prefer to use python scripting outside the ArcMap, the "Make Image Server Layer" tool must be used to convert the image service URL address to a in-memory image service layer. The layer then can be used as input in the spatial analysis tool.
But please beware the output size of the raster you can get from image service is limited by the service properties, default is 4100x15000.
If you can provide more information about how you get this all-nodata result, I may be able give more suggestions.
Thank you!