I'm of two minds about what will happen with the Hokage role if Tsunade dies.
If I remember correctly, a Kage is chosen by the village council and okayed by the daimyo. It's not Tsunade's decision -- or a strictly military decision -- who replaces her, and I don't remember it ever being a literal battlefield promotion. Even when Kakashi thought he was going to become Hokage before (during Tsunade's coma), he had to return from the field first and meet with the elders, etc., before it was official. So that seems like the precedent that's been set, which might indicate no Hokage will be chosen immediately.
On the other hand, Kishimoto may decide it must fall to someone to act in that role mid-war and if he does, I think it has to be Kakashi because he was selected and technically promoted before. The formal process was already undertaken, and he was accepted as the logical replacement for Tsunade.
And really, there's
so much potential in that decision, in terms of the conflict between Kakashi and Obito. I mean, we know it was one of Obito's youthful ambitions to become Hokage. Imagine if he somehow witnesses Kakashi's field promotion to that rank? Especially if he were to also know that Rin had loved Kakashi as well?

*shudder*
We know Kakashi doesn't want to be Hokage and perhaps, if he survives, he would officially cede the position to Naruto later as confirmation of Kakashi's stated opinion that Naruto has surpassed him. And in my view Kakashi's death is not necessary for Naruto to obtain personal growth; that kind of hero's loss was achieved through Jiraiya's death.
For what it's worth, Naruto's growth trajectory reminds me a lot of Harry Potter's:
Harry's parents die protecting him --> Sirius Black, closest link to his parents dies --> Dumbledore, authority figure dies --> leaving Harry to face Voldemort with a few adults and his rookie friends.
Naruto's parents die protecting him --> Jiraiya, closest link to his parents dies --> Tsunade, authority figure dies (?) --> leaving Naruto to face Madara/Tobi/Sasuke with a few adults and his rookie friends.
It's a lot like Frodo's progression too, for that matter. Not that Kishimoto will do exactly what Rowling or Tolkien did, it simply illustrates a common "hero's path" in literature. However, I'm reasonably confident Kishimoto will not exact as much collateral damage as Rowling. I just don't see him killing off half his characters in the final battle, including Kakashi. But I have been wrong before....
Regardless of what Kishimoto is doing with Kakashi within this arc, I don't see Naruto becoming Hokage right now for a variety of reasons -- some logical constraints within the story, and some implied authorial intent on Kishimoto's part.
A lot of it depends on the importance of some of the deeper themes in the story. If Naruto is truly a messianic hero who will unite all the clans and all the lands into a more harmonious, homogeneous culture -- if Naruto were to, say, end up the reincarnation of the Rikudo Sennin and jinchuriki of the Ten Tails -- would the shinobi world still need Kage? Maybe Naruto will never become Hokage because he'll already be too far above it.
Just my rambling thoughts for the day.