In most cases you are able to do the recording. However, you wont be able to do a gateway style recording. Instead you will have to select the proxy recording setting to allow the additional interaction between services to work. Some services using CORS, you may need to register your VSE's recorder IP address with the system you are trying to record to avoid restrictions that could prevent CORS from working.
If you still have issues with trying to record a CORS based service by selecting the proxy recording setting, and registering the IP address of the recorder with your application, then reach out to our support for further guidance.