alt Hacker Newspossibly counter to intuition, I find that since I have started to religiously use my stationary bike in the morning, I have a lot more energy for the day, not less. I suppose if you're butting up against caloric/nutrient limits you might suffer. I personally find exercise clarifies my thoughts and improves my mood, even if its the last thing I want to do when I do it.
The mind-body connection is quite real. Improving your physical state will almost certainly have a non-zero improvement on your mental state. Exercising can really help you make sense of all those other things you have going on. Not to mention that being in shape and strong makes every physical thing you do easier.