Yes, after Sasuke woke up in the hospital and saw how strong Naruto had gotten, he had indeed gotten the idea in his mind that Naruto had managed to suddenly surpass him. That combined with the fact that his brother had defeated him again and had told him again that he was not strong enough was, I think, the trigger that finally made Sasuke give in fully to the Curse mark. I believe he tried to fight the effects of the mark at first, but after seeing how strong Naruto had gotten in a short time and having his brother pointing out his weak points again, he probably thought that giving in to the Curse mark would be benificial to him. He decided to take the risks, involving the usage of the Curse mark, just so that he could get more power and stay ahead of Naruto.
But all in all, I believe it was the Curse mark that actually contributed the most to making him leave the village. He seemed content with the training he received during his time with Team seven (he probably would have demanded for more severe training later on though) but it was only when the Curse mark showed him what he could accomplish when he used the power that the hatred grew stronger and ultimately took over, though it apparently didn't cloud his mind wholly, as shown by his refusal of killing Naruto at the Valley of the End after Naruto had lost consciousness.