Android : Can I use Google Play Services' multiplayer to make a quasi-turn based game?

I would like to use Google Play Services in my next multiplayer game which will work as follows:

One player will start a game with several others and that player will set a highscore. This player passes their turn on once they have set an initial score, allowing ALL of the remaining players to take a turn at setting a highscore (potentially simultaneously) while the "highscore" player waits to be overtaken.

Is this possible with Google Play Services?