I doubt Kakashi would have done much with his skillset, not to berate Kakashi, since I'm a Kakashi fan, but I don't think his jutsu would match a gigantic monster like Kurama, judging by what we've seen(This excludes Kamui since he couldn't activate his Mangekyou at that point)Plus his lack of stamina prior to Part II,
Itachi was only a child, he didn't even awaken his Mangekyou yet, and his skillset doesn't seem to match giant beasts, only Susanoo could do that.
If Gai was there though, Kurama might have died, due to the 8th Gate(If Gai could even use the 8th Gate then)