There's a big difference in ketosis and ketoacidosis, not just in the quantity of ketone bodies, but the context. For diabetics, the presence of large amount of ketones (ketoacidosis) indicates that the body cannot use glucose as a fuel source, even if its present in large quantities. This indicates that insulin isn't working and the body has to break down protien instead, which are your muscles. This is very bad. You have large amounts of blood glucose, which damages kidneys and eyes etc, and you're breaking down your muscles, which is never good long term. Let me repeat: This is bad.
Ketosis, on the other hand, is actually a normal phenomenom. Your body is designed to switch fuel sources fairly easily, although this ability has been diminished with our non-stop carb intake. Ketones are produced when your body breaks down protein, whether its from diet or your own body.
The misconception that paleo is a more natural sourced Atkins diet raises a lot of (unfounded) fears of ketoacidosis. First off, the emphasis on fats and veggies instead of unlimited proteins usually doesn't kick off ketosis on a regular basis. Periodically, I'll get some ketone strips for analytical purposes to see what my body is doing, but not to try to get into ketosis. What I have observed is that I almost never get into ketosis, and if I do, its slight.
Another ketosis factor is exercise, which is part of the paleo lifestlye (NOT A DIET!!). I am never in ketosis immediately after exercise. Why? I've just used all the fuel! If I don't eat anything for a few hours, it'll kick in big time, but I almost never do that.
Now, as far as the brain using glucose... Your brain can use both glucose and ketones for fuel, EXCEPT for some small parts of the brain which needs to use glucose. The amount of glucose needed to fuel this is about the same that your liver can produce from protein. Pretty convenient. You're in school, look up the amounts.
To answer your question, No. The chances are minimal, if non-existant, that you'll get into ketoacidosis on a paleo diet/lifestyle.