It's entirely possible that if you're on "Fire" it'll have a fire effect/be of that element, damage-wise - same attack, different graphics. I agree that it's likely unrelated, though. However...
That's what I'm curious about. Let's say Robin's jab uses a Tome - Elwind, for example. You've used up your Elwind and Robin's tossed it away. Do you still have it for your jab? If so, it's strange that he tossed it away just a moment ago but can still pull out another copy. But if you can't use it anymore at all, including your normals, what happens instead?
In general, though, I'd guess that your Tomes only last for your stock. Which should have some interesting gameplay - missing your Thoron would be WAY bigger than missing your shot with Samus. Spending too much time mid-air trying to edgeguard leaves your Elwind empty for when you have to recover. That sort of thing.
Another idea is that you'll just be seriously gimped - you'll just have access to the E-Rank versions of the Tomes. Wind, Fire, Thunder, Flux. You can still use your specials but they're all worse. Thunder wouldn't be chargeable, for example. That seems less likely to me, though, since they specifically tied the Thunder ranks to charge power for his Neutral B.