Can an Adobe AIR app that's running in the system tray pop up a window?

Question

For example, if I were to write a calendar app on top of AIR, say with Flex, could this app pop up reminder windows for approaching appointments, just like Microsoft Outlook can

Answer 1

Twhirl pops up "toast" notifications (similiar to most instant messengers), while it is running in the system tray.

So yes.