I think you are asking which thread will the RealTimeMessageReceivedListener
async callback run on. As far as I can tell, the callbacks will run on the main Android UI thread (*1). This thread is different from the Libgdx main UI thread (*2).
This means the Google Play Service callbacks can run independently of your main Libgdx logic. If you have your GPS callbacks use the Libgdx Application.postRunnable API, you can get your main Libgdx thread to deal with all the incoming changes serially with everything else (queued runnables are executed at the beginning of each render loop).
(*1) search for 'thread' in this Google Developers blog post. I couldn't find any better reference.
(*2) http://www.badlogicgames.com/forum/viewtopic.php?f=21&t=1298