With mozilla, proxies are only used on the ports you specify [*edit: what I mean is, you have options as far as what you want the browser to send to a proxy. I mainly use FF so this is what I can tell you.] If you set up a SOCKS proxy, then all socket connections would be routed through that -- including, I'm almost positive, any socket connection originating from a Flash program. If you only set up an HTTP proxy, then only communications with HTTP headers going to port 80 somewhere would be sent through it.

The browser proxy settings are the first line of defense and can be supplemented by the network settings on the machine or the router. Similar situation there.

Best way to find out is to download Tor or Privoxy, set it up in your browser and test it against your server...