Thanks for all the replies chaps. Devlin - your description sounds like how I imagined things were. I don't like programs running that I don't need, so connecting directly sounds like what I would want.
I have a further question about the SSID - I've read lots of stuff about turning it off so your router doesn't show up, which I can understand. But how does all this hang together? If the router is not broadcasting its SSID, what is your PC using to connect to it? And can you connect another PC to it while it is off, as presumably that PC is going to say it can't 'see' it?