What do you mean by "new mails added to them"? I have Thunderbird set up with old emails I imported from Outlook Express in local folders and it seems to work fine. I don't really add new emails into them very often but I'm pretty sure it's fine?
I mean another application than Thunderbird is adding new mails to the mailbox. Which is the classical purpose of a mailbox. In my test Thunderbird had not recognized the new mails, and I'm not sure whether I just did something wrong, or Thunderbird does not have this ability anymore. After all, they don't offer local mailboxes in their account-settings anymore.