Yes, you can.
Many different third-party systems can be seamlessly integrated with a CBus automation system. The range of network units and be used to communicate on many different protocols including: OPC, DALI, DSI, DMX, BACnet, Pascal, TCP/IP, Control4, Crestron, AMX, RTI, LonWorks, ModBus, and many more.
Specifically with Control4, one of the most popular methods is to utilise a CBus RS232 network unit and configure it to act as a permanent bridge between to the two systems.