Even if his Sharingan could see Naruto coming, he still doesn't have the reflexes to take any action if Naruto comes from behind. It might wind up being the same as when Sasuke first faced Lee. Even if Sasuke's sharingan was able to see Rock Lee's movements, he didn't have the reflexes or speed to react in time.
The Sharingan doesn't increase one's speed. Just because Obito was capable of keeping up with them doesn't mean Kakashi automatically will. Since his own speed and reflexes would obviously have to take part as well.
Though if Naruto happens to stop for a moment or slow down for any reason, Kakashi could take advantage and use Kamui then. Since Naruto won't be able to come back from that dimension. That's ofcourse, if it happens before he dies or runs out of chakra.