The biggest weakness of that rushdown strategy is you have limited ability to assassinate troops from actual opponents, and with the small 2p board the opponent can severely slow you down if they block off parts of the board to prevent you from placing all your troops, then beat you at the long game by going Ambition.
Yeah that has been my experience when trying to go for an agro/rushdown deck. What makes matters worse is the ambition deck is likely to draw into more money so when the really good expensive aggressive cards come up the ambition player has a greater chance of acquiring the card.
The PvE style deck mentioned by veector might be more likely to work then trying to kill the other players troops. Because in the Drow/Demon deck there some to be a lot of assassinate a white troop style of effects. Will have to give this one a try if possible.