If startup application on your Real-Time controller communicates only with FPGA and not with the Host PC, application will work also without physical connection (Ethernet/USB).
When you reference your FPGA target ("Open FPGA VI Reference") using an IP address, the information sent to and from the FPGA goes through the RIO server, which requires going through the network using TCP/IP.
If your application doesn't work without physical connection, you should also receive an error on Real-Time Controller:
Error -63043: The session is invalid. The target may have been reset or rebooted, or the network connection may have timed out because of processor overuse. Check the network connection, reduce the demand on the processor, and decrease the timeout of the operation that failed.