Is there a way to customize the popup notifications for Empathy in Ubuntu 12.04 so that instead of displaying the message contents and the sender, they only say "New Message" or something like that? I know that there are some ways to modify the appearance or behavior of popups, but I haven't seen anything that would do this yet.
What you want is not to suppress the notification but to show a custom message instead.
Unfortunately, to my knowledge, the is nothing that mimic that specific behavior. Using gnome there are extensions like the following that modify the look/display of the notification, find this one here.
If this is not to your like pick one and take a look at the source code, you could probably work something out.