I'm basically a night owl. So if I'm left without a schedule, my sleeping hours drifts naturally to about 2AM to 9AM. That's what happened in college.
Now that I'm working, I wake up at 6:30AM and go to bed at around 11:30PM. However, just because I get up early, I get next to nothing done before 9AM, no matter how much I sleep or when I sleep. My metabolism just doesn't kick in at all until after 9AM. I also can't eat anything 95% of the time before 8-9AM without feeling like I want to throw up.
I've noticed since middle school that my energy peaked in the late afternoon / morning evenings, and it still does. I typically can get more done in those hours than the rest of the day. And I was worse in senior year of high school, going to bed at 3-5AM and getting up at 9:30AM (my first class in senior year was 3rd period at 10:30, because I only needed 1 class my senior year). Thinking back right now, I probably had trouble in school that year because that's when my sleep cycle hit the extreme. Thank goodness my rankings were frozen towards the beginning of that school year.
But to answer the op, no, I definitely do not get more done if I wake up earlier. I'm pretty much a zombie the earlier it is.