I would pay if it were something amazing (i.e. not just a bit faster than Thunderbird), probably around $20. I don't spend that much time on email, but I hate the small annoyances of Thunderbird (when I delete messages a new, empty one appears that can't be removed, it has no tray icon, it starts up maximized and I have to close it every time, it has no decent "send later" functionality, etc).
These are all things that Thunderbird doesn't get right. Also, search is completely broken.
I've got a tray icon in Gnome Shell (and I had one when I was using Gnome 2), using the FireTray extension, and there is also a Gnome Integration extension that provides a tray icon, in theory, but it doesn't work for me.
The little icon biff-like that shows if you have new mail? I always thought it was fairly useless. One or two active mailing list subscriptions and the icon was always lit up.
PS: What is the signifigance of the italicized is?
'notification area' is a little bit more generic a label. If your OS has a global status/taskbar of any kind, it's usually on the right hand side of it.
These are all things that Thunderbird doesn't get right. Also, search is completely broken.