Yes! And No! And Yes!
Problem: What is 100% happiness, what does it look like? Does it just mean that you have 0% of other emotions, or that your happiness is a certain percentage of total bliss, which would be 100%? How could you measure it. Does happiness have quality? Could you have bad happiness and good happiness, and if so, which one counts? If you are 100% full of bad happiness, then what? What happens at 100%? Are you full? What happens if you are at 100% happiness and then you get happier?
These aren't meant to be answered by the way.
I find the problem is with the question. Is it possible to be genuinely, positively extremely happy? Yes. Can you be this all the time forever and ever? Nopes, because that's not the purpose of feelings. Can you be grateful for the world and enjoy every moment of it, through happiness, sadness, and everything inbetween? Sure can!
From what I've learnt, it's not important how happy you are right now, because that will change, what is important is increasing your happiness, which means increasing the quality of your life. I don't mean getting new stuff either, like a bigger boat or faster TV. I mean going out there, enriching your life, conquering challenges and accomplishing true and deep goals. This will enhance your life, and improve it overall. You will be happier for a much longer time.
Can you be 100% happy? Wrong question. Can you become happier all the time? Yes!
Ultimate question: What can you do right now that would improve your life and lead to increased happiness?