I have about a dozen email accounts in Thunderbird. It polls them for mail and gets it for them all. Notifies of new mail and shows unread counts in the folder pane. But beyond that I really don't think I understand your question.

okay, so the answer is yes, that's great news.

I've been monitoring this account, works great. However, I added a "new" account, it acted like it took it, but it's not showing up. Maybe it's because of years of using Outlook or something, but I'd expect it to show up as another inbox...?

So I guess the expanded question is: How to make it see multiple accounts?

I assume you added a pop mail account. It will just be included in the global inbox in local folders by default. Only IMAP accounts get their own entry and that is because each folder is syncronised to the server, not for any other specific reason.

You can force the issue to have a fully formed account with it's own folders by changing the settings in the advanced button in account settings > server setting to use it's own inbox. Personally I like only having one inbox to look at and one sent folder.

Personally I dropped using Outlook about 2004. As soon as Microsoft introduced their ribbon toolbar, Office went with it. I have not looked back except to do occasional projects in Excel building templates and macros, so I struggle when folks compare with outlook. I have no frame of common reference in that product to refer to.