It's written in Java using the Dropwizard framework.

I've skimmed through the code and found references to Protobuf, GCM and Redis

It's open source so you can check the code here: https://github.com/signalapp/Signal-Server

It looks like mostly blocking code... I wonder if that's hampering their ability to scale.

Java. https://github.com/signalapp/Signal-Server