Is it possible to receive the CCMS alerts displayed in the transaction RZ20 in the PI alert inbox (or vice versa)?
Yes. By using an auto-reaction method (CCMS_Send_Alert_to_ALM), you can have alerts from the CCMS automatically forwarded to the PI alert inbox. Conversely, you can have message-based alerts forwarded to CCMS. You achieve that, you use transaction SM37 to configure a background job (SXMSALERT _PROCESS_DATA_GET) which does the forwarding. In addition, you can configure PI message-based alerts to be forwarded to the alert inbox of the SAP Solution Manager 7.0.