We train inside and put a relatively heavy armour on. Just being at the dojo makes you a sweat a lot especially in summer. It is very common in Japan that many people get dehydrated from training. Even when you think you are fine, the dehydration can lead you to get injured severely.
It was different back in old days. When I was young, I was not allowed to drink anything until all
the training session was over. However, when sports science kicked in to the
kendo world, kendo training has changed a lot. Yes, it is very important to
keep ourselves hydrated; otherwise, we end up with severe life threatening emergency,
especially in summer.
* I am not a doctor. I am writing this article through my experiences and what I learned from doctors I have seen. Please read this as your reference.
Some might think as long as you drink some fluid, you should be fine. But it is not very true. Do not consider fluids that contain caffeine such as coke or coffee since they act as a diuretic. You still can drink them but make sure that you drink water as well.
If you sweat a lot, it is not only water inside your body you are losing. You are losing electrolytes such as sodium as well. So you have to regain not only water but also these electrolytes.
Certainly the drink in the photo (The original uploader was PeteVerdon at English Wikipedia. / CC BY-SA [https://creativecommons.org/licenses/by-sa/2.5]) looks very attractive especially after training in humid summer. But probably I don't have to mention this, beer tastes so good after training, it doesn't help much with hydrating you after having sweat a lot. I am speaking from my experience so I am not sure if it is medically true or not. Well, it does sound very true...
Have sports drink (Gatorade is well-known in USA. Pocari Sweat in Japan) ready when training. For a long training such as training camp you should not forget to have fruits.
You should keep yourself hydrated so you might want to keep drinking sports drink during training especially in summer.
If you are an instructor or play an instructor role, it is a good idea to make your kendo mates to drink sports drinks when they can (after suburi or during a break).
Hope this helps.