Is it possible to gain enough Crowd Favor in the colosseum to win in a single round? I'm inclined to say no, because it doesn't seem like there's enough going on, even with a 5-hero team, to get 20 points that quickly right off the bat.
Kaargra plays Get Back In There and Bloodsworn Judgement. This puts Kaargra in play, and attaches Chaos Lord to her.
Now, every time Kaargra is dealt damage, she plays the top card of her deck. This means that by the fifth turn, Kaargra could have as many as 5 gladiators and herself in play, with an option on one more. Legacy Galvanizes, and on the fifth turn, Unity Hastily Augments O-X's Defensive Blast, to deal 4 damage 4 times to 6 targets. That's 16 damage, and more than enough favor to guarentee the victory, assuming that you also kill Kaargra.
To kill Kaargra at this point, you need to have done 24 damage to her already. Legacy uses Galavanize and Inspiring Presence. Chronoranger plays Eye On the Prize x3, Displaced Armory for his Hat, Displaced Armory for Compounded Bow. 7x3 = 21 damage. Then Ra plays Fire Blast.
And that's without pulling in the Scholar for chained Don't Dismiss Anythings.