Can you appeal against 2 yellow cards?

Yes.

A player can be shown a direct red card in Association Football (called soccer in the United States) if he has committed a serious enough offense; e.g., a two-footed cleats up tackle or an intentional or flagrant foul on the opponent.

Absolutely.Think of it this way. If a player has been abiding by the rules during play but at a given moment commits a major foul which, in the opinion of the referee, warrants the issuance of a red card, the player can get a red card and be sent off without having gotten a previous yellow card. Here's a "for instance" to illustrate the point. It's from an actual game. A player shoots on goal, but is a long way out, and the keeper has time to react, lunge wide and get both hands on the ball. The keeper pulls the ball to the chest with both hands and curls up because a striker, who was running full speed toward the keeper when the shot was taken, is three or four steps away. The striker, who had been playing fairly throughout the game to this point, inexplicably slides into the keeper, who is lying on the ground curled up in a ball. The keeper is injured. The referee, who was perfectly positioned to see the play, determines the striker had more than ample time to avoid the keeper, and, in fact should have veered off or jumped over that keeper. The referee immediately blows his whistle, runs to the spot and shows a red card to the striker, who is then sent off.

FIFA Laws of the Game

Law 12 - Fouls and Misconduct

A player, substitute or substituted player is sent off if he commits any of the following seven offenses:

1. serious foul play
2. violent conduct
3. spitting at an opponent or any other person
4. denying the opposing team a goal or an obvious goal-scoring opportunity by deliberately handling the ball (this does not apply to a goalkeeper within his own penalty area)
5. denying an obvious goal-scoring opportunity to an opponent moving towards the player's goal by an offense punishable by a free kick or a penalty kick
6. using offensive, insulting or abusive language and/or gestures
7. receiving a second caution in the same match