There is no random race selection out of the three main races, but however, you can still 'fake' additional races by allowing them to be selectable through dialogues, changing starting units and tech tree as well as customizing the UI. I'am not too sure about randomizing races but you can look into the Random selection triggers of the Allied Commanders Mod for a better idea.
Somehow Desert Strike Azure does it. You can select Random in the lobby and in game it knows you selected Random. I was thinking of creating a new race named "Random" and then just doing the rest with triggers - but I wasn't sure how to remove the existing Random selection from the Bnet lobby.