Full duplex communication on a TCP socket

Unless 'continously' means the server is flooding the socket with data and is using most of cpu time, full duplex communication is possible; as a matter of fact I dare say it's a common situation with TCP sockets.

You must also consider your physical layer and link level. Some transmission media is inherently half duplex, although I think you are using a 100Mb or Gb Ethernet interface which both support full duplex transmission.

With Nios these lower layers are normally not a problem and the bottleneck is the software side (TCP stack management and application).