Yes you can!
When a contest goes live, check under the badges of each game for a button that says "watch live". It looks like this:
Just click on the WATCH LIVE button, choose your streaming platform (twitch, youtube, or anywhere else the game is being streamed) and the game will start streaming! It will look like this:
If you want to hide or close the stream at any point, press the HIDE LIVE STREAMS button and the contest will go back to the default display.