No, he's PINING for 'Jeanie' at this point. He actively considers himself in a tussle with Summers for her affections, which Jean kinda-sorta reciprocates. It's clear she loves Scott, but Wolverine's bad boy nature appeals to her more than she likes to admit. But that doesn't make her 'his woman' in reality. Notice that Scott and Jean have run out together and Wolverine has just shown up alone at her apartment.