I drilled into the young coconut and got a lot of juice. Can I drink all of it without anything bad happening?

Yes. Coconut has gotten a bad rap, primarily because of its natural saturated fats. However, it is quite healthy and was a major staple on polynesian diets. Enjoy! just don't overdo anything. I personally drink coconut juice!
Thirst quencher. I would also add to the excellent comments left already that coconut water is far better than gatorade, powerade, or any other sports drink for rehydration without excess sugar. It's loaded with vitamins & minerals. In addition, it's an excellent part of a hangover therapy. If using one that's pre-packaged, get one that's pure coconut water like vita-coco.
Yes. Coconut juice is very nutritious and has a chemical composition similar to human plasma, therefore, it is full of vitamins and minerals, low in calories and can give a sudden burst of energy. Enjoy!