NAS is just another device plugged into the router, and can be accessed as you would access another computer.
I doubt, but am not sure on this, that TBird is designed to be run as a networking app, so you wouldn't be able to have multiple copies of TBird working with the central set of data files simultaneously. However, when you checked and replied to your mail from one machine, if you then used a second machine later, it would have access to the current data set.