No, instant action is offline gameplay. In order to play online you will have to use the Renegade X server client, which also came with your installation. What you have to do is (double-)click the Renegade X icon on your desktop, this will open up the server client. Now choose a server from the server list, last time I checked there were 3 servers online.
Pick one of those servers, hit the connect button and get ready to play. It is currently very rare to encounter other players, this is due to the fact that the current release of Renegade X has been out for almost 2 years. Most people are waiting for Black Dawn - which will no longer require Unreal Tournament 3, making it a standalone indie game.
There are people online from time to time and all I could suggest is checking the server client every now and then, or checking the top part of the forum which shows how many players are playing Renegade X. I mentioned this in episode #7 of the Renegade X Community Q&A: http://www.youtube.com/watch?feature=player_detailpage&v=8hXUqjGv56I#t=277s