Your description fits to the 10BASE5 Ethernet AUI interface (looks like RS-422) between the Ethernet card and the vampire transceiver puncturing the thick yellow ethernet cable. Those control signals carried the carrier sense and collision detect signal to the actual Ethernet card.
Other than that, I have never seen a protocol using the RS-485 hardware to rely on the media access unit monitoring the bus for bus access. The access is typically controlled in software either by the master/slave relationship or token ring/bus systems.
OK, there is one historical curiosity, before actual CAN bus transceivers were widely available, ordinary RS-485 transceivers were used by controlling the TxEnable pin with the dominant/recessive information. The bus arbitration was handled by the controller by listening at the traffic on the bus on a bit by bit basis, but this did not use the RTS/CTS control.
Paul