KissmeWhat Lange said.
The only question I would have is, once someone signs up for the PUG through the website GUI, how would the IRC bot go about adding another user to the IRC channel with the correct name? Maybe if you could make an alias for yourself like on TF.TV, so once you log in with your Steam, it recognizes you and gives you the alias? I guess finding how the two would 'mirror' each other would be the hardest thing in my opinion.
You could have someone sign in through steam, set an alias and then join the irc channel under that alias
and if they want to play they can fill out checkboxes on what classes they want to play, then it sends the !add command with the classes.
to see which classes are already added you could have the pug bot send a parsable string and do that client side in the browser