When using the REST API, normally one can see which OGC extensions are supported by the service, under the supportedExtensions property. But this does not appear to be the case with image services- the supportedExtensions is not included.
Is there any way to determine, using the REST API, whether a given image service has OGC types enabled?
If you browse to the REST endpoint of the image service, you should see the OGC capabilities listed in the upper left-hand corner.
As for through the API, I couldn't find anything exposing the extensions in :6443/arcgis/rest/services/serviceName/ImageServer. However, if you look in the admin services directory, there is a parameter "extensions" that lists out all of the extensions exposed on the image service.
This would be formatted: "admin/services/serviceName.ImageServer?f=pjson"