No, this currently isn't possible - Unity can send the voice mail/email/fax message counts in your inbox along with the body of the email there but it's not possible to include specific information about a specific message.
The notification engine is actually setup to trigger on one or more message types in the inbox, a notification is not strictly tied to a specific message in your box. So when the notification engine picks up and does its thing (either sending out an email, tone page, SMS or calling out on a phone line) it knows only that a particular trigger was tripped (i.e. an urgent voice mail was marked new in the inbox) not which message it was. It can snag information about the inbox (the message counts noted) but it doesn't have more details than that.
We could "fudge" this by, for instance, getting the most recent message that matches the notification device's trigger rules and including that detail in the body, but this would have windows of opportunity to screw up (i.e. if multiple messages of the same type came in at about the same time).
It's a little trickier than it may sound on the surface since the message store is out of our direct control, we only get notification of changes.
