Recently watched SAO, on wiki it says "Even though Kazuto had decided to go to school in America for the summer to pursue his mechatronics career, he asked Asuna to accompany him overseas, as he could not live without her, even if it was a very selfish desire. Asuna replied that her answer to that question was decided a long time ago."
http://swordartonline.wikia.com/wiki.../Relationships
Does this happen in the anime?