Yes, you can do that. There's a difference between a Facebook Application and a Facebook Page:
* Your website (Joomla) requires a Facebook Application to be setup. This is what let's JFBConnect fetch information from a user's profile, post to pages or do any other interactions with the Facebook platform.
* With an Application setup, you can setup as many 'Channels' as you want to connect users that have authenticated to your Application to Pages that those users administer. Each channel lets you post or read from that Facebook Page after the user has give your site/application permission to do so.
So, get started with setting up your Facebook Application and verify that authentication works on your front end. Then, create Channels for each Page you want to be able to post to.
I hope that helps explain, but if you need further details, just let us know!
Thanks,
Alex