Is there a complete conversation convergence app?
Many have tried.  It's arguable whether anyone succeeded yet or not.

The big ones are Motorola's MotoBLUR, HTC's SenseUI, Samsung's TouchWiz - they all try to bring together the disconnected social aspects of different applications such as e-mail, text messages, and various social networks.  Each does it differently, with varying degrees of success.  Unfortunately these aren't stand-alone products.  They usually come pre-installed with their respective manufacturers' devices, and overhaul more than just social aspects.

There are also 3rd-party apps and widgets that attempt to do this merge.  One of the best that I've used is SlideScreen. I didn't like the fact that it replaces your launcher, but it sounds like exactly what you're looking for.