I'm personally a Neji fan, but I doubt he'd be able to learn Chidori. When Kakashi said Byakugan had better "insight" than Sharingan, I think he meant that it can see things with greater detail and focus than Sharingan, but it doesn't provide the auto-counters that Sharingan does through the "dot" things.

Also, with Rasengan, I guess any genius ninja might be able to master it given time, but Naruto was able to learn it quickly because he's using his own improvised method involving Kage Bunshin, which none of the genins have access to. Maybe after years of practice Neji might be able to master Rasengan, but we'll have to wait and see.