I've tried to run a campaign via IRC, but it didn't work well.
Players can be easily distracted and you don't even know until you notice they are lagging. They are also more prone not to take it seriously, not showing up at all. Finally, they can experience technical difficulties.
I wouldn't ever consider it again unless I've really got no other option. Since, as you say, you have got no other option, I'd say go for it. It's quite easy actually, since you can create and lock a channel on pretty much any server, and clients exist for any relevant platform. You just have to find the players, but since the Internet is very large you should have no problem finding them... the problem is more finding good, reliable players; I can't help you there, but I have some more advice I hope will help you.
1) This is vital: build an atmosphere, something really cool, which players really care about, that will hook them to the story. Since it's much easier to lose them on the way, it is much more important to give them reasons to pay attention.
2) Keep it simple: if players start not understanding you, you'll lose them.
3) Use the moderation when you describe something, removing it only when you are done with the description and players are allowed to talk.
4) Remember you can easily have private chats. This is the biggest (and only?) pro of using IRC vs. doing it IRL: since it allows you to interact privately with players without other players knowing, you can develop cool stuff with it if you are a bit creative.
5) Know intimately the setting, and be prepared to react instantly to the players' actions. IRL if you "lag" players may chat and as soon as you are ready you can immediately get their attention, while on IRC if you lag... they open a new browser tab and start reading other stuff somewhere.
6) Give the players a strong and believable reason to be together, and if they somehow split up, keep all the non-important-private stuff public: even if you just have two groups that would mean that every player would get 50% time wasted, and that would instantly lead to distraction.
I know some of these rules contradict the others, but, well, I've never said that would be easy.