Note the comments in two other bugs now marked as duplicates of this one. In particular, bug 545113.
In particular I can confirm that I see no notification or indicator change if mail comes in while I'm sending a new mail with a full-screen window. That seems problematic since I'd particularly like to know about incoming mail when I'm responding to an active thread. But I think that should be a separate bug, and it would be nice to be able to file that bug after seeing what the documentation says should be happening.
Note the comments in two other bugs now marked as duplicates of this one. In particular, bug 545113.
In particular I can confirm that I see no notification or indicator change if mail comes in while I'm sending a new mail with a full-screen window. That seems problematic since I'd particularly like to know about incoming mail when I'm responding to an active thread. But I think that should be a separate bug, and it would be nice to be able to file that bug after seeing what the documentation says should be happening.