We have a scenario where we should send data from SAP ECC through PI to Tax Authority where SAP ECC would talk to PI with RFC, and to the Tax Authority PI should send data with REST API.
We have a tool in SAP ECC that can create the XML in the structure required by Tax Authority. So it would not be required to modify, map, translate anything within PI.
Is there a way to send XML "string" in RFC from SAP ECC to PI, not mapping it, and sending it further with REST API?
Response from Tax Authority would need to be sent back to SAP ECC as a return value of the RFC call.
Is this all a feasible solution without mapping?
Several ways to achieve what you want, the easiest solution would be to create a mapping which is required that simply maps the XML string -> XML string, this would mean you technically have a mapping but it does nothing.
You could also look at direct connections (see https://archive.sap.com/kmuuid2/b00bbb77-75bc-2a10-6b9a-a6f8161515a6/P2P%20Direct%20Connection%20Design%20and%20Config%20in%20SAP%20using%20NW%20PI%207-1.pdf) which would not requrie a mapping but the setup might defeat the simplicity you are looking for.
Hope that gives you an idea. You can see plenty of articles on SDN related to Direct Connection in addition to the PDF link I included.