They're probably so far removed that it doesn't really matter...but imagine the power of Byakugan and Sharingan together. No way to avoid eye contact when you can see all around.

Still, I believe him and Sakura are kind of destined...if it's gotta be any of the girls it will be Sakura. She has shown affection for him, and when he finally kills Itachi (who knows if that will happen), maybe he'll mellow down and actually see this