Well in the second movie they kinda kiss soo I'm guessing yes by the end of the series
either Khugo or Segome.
At one point he did, but he forgot about her. Her name was Ayame and when they were little they promised each other that they would get married under - I forget what it's called but I'll take a swing at it - the moon's rainbow (I think 0_0. I lied, I'm really unsure) The episode is a filler (meaning it isn't an important episode) and it's when Ayame comes to marry Koga, but he refuses and sticks to his love for Kagome.