He'd be screwed. Kakashi is pretty much dead at this point, and having to fight the Juubi would just make his death that much quicker. He's been worn down at least twice during the war arc, and his fight with Obito probably burned up most of his chakra. Kakashi likely doesn't even have enough chakra left to get out of the other dimension.
On a side note, though. What if Kakashi has been trying to get back to the battlefield for a while now, and Obito has him trapped in an infinite Kamui loop? Imagine if Kakashi was just stuck between dimensions now.