I'm fairly certain that you don't need any outgoing ports open to get connections - can you connect an irc client on your work network? That's the primary way that the client gets new connections.
Why not just run it at home?
No, IRC is port 6667. It's blocked, like I said in the first post. Since I manually pointed the client to a server using -addnode, I'm assuming whatever other port it uses is blocked as well.
And I was planning to run it at home, but I'm at work now, and I wanted to try it out. Plus I figured since my work machine has to stay on 24/7, it might as well help out generating bitcoins instead of just idling... but obviously that's not going to work.
Well, if it can't do it, please make this a feature request... I find it a little unbelievable that this feature doesn't already exist, though!