Do you win a game of Catan even if you don't realize you have won?
I have found reference to this in other posts, though I didn't see a question phrased as directly as this.

In reference to the online Rules (PDF):

On page 5, you will find the following under "Ending the Game":


  If you have 10 or more victory points during your turn the game ends and you are the winner! If you reach 10 points when it is not your turn, the game continues until any player (including you) has 10 points on his turn.


There is no requirement of declaring victory (though in other parts of the rules it does use the phrase "claim victory" or something similar.

On the online FAQ the question is addressed pretty directly:


  Victory Conditions - What if someone has reached the required number of victory points for a win but is unaware of it? Did this player win anyway?


With response:


  Yes. The game ends as soon as a player has reached the required number of victory points on his turn. If he’s unaware of it, you should tell him, because you can’t take an already gained victory away from him.


And on another FAQ page you are not allowed to not claim victory to "pad" your score in an official game:


  Victory Conditions - May I continue scoring points after having reached the number of victory points required for a win?


With response:


  This could make sense in a private tournament where the scores from several games are added up. For individual games and official tournaments, the following applies: You have won as soon as you have reached the required number of victory points on your turn – and then the game is over.


So, if you want to run a private tournament with some "house rules", you could, but in an official game the first player to have 10 points on their turn wins, regardless of if they realize it or announce it.