Every time I try to launch a single-player game, be it tutorial, scenario or custom, my firewall notifies me that joshua.exe is trying to connect to the internet. If I don't allow this connection I am returned to the main menu with a notification that the game could not connect to the server, and thus I cannot play unless I allow the connection.

As I am only playing single-player at the moment I don't need the game connecting to the internet, is there some way to disable this requirement to be online to play?

Yeah seems so, I also read a thread over on Steam involving one of the developers who explained that:

"even in single player mode, the game creates a server on your machine. If you look at the task bar, you'll see two applications running - the SP2 client (the graphic window) and another top-level window called "Joshua". That's the game server. Single-player mode behaves in every way like a multi-player game, except that your server is local and locked to just yourself. This enabled us to use a single communication pipeline for every game."

I'll just add an exception and that should be that.