If your overweight of course exercise will help you will look alot better and feel good about yourself and proberly get more girls

But unfourtantly exercise and the correct diet will do nothing if you have gynecomastia with glands behind your arolea.
Although as you say you could just be overweight cause you to have moods which would then be pseudogynecomastia not gynecomastia.
Recovery fully is around 1 year although this depends of the person everyone is diffrent.
You will need at least 1 week post op to recover.
Its not painfull post op maybe a little uncomfortable with the vest on e.c.t.
My advice to you and im not doctor, is to get in shape first as if it does feel like just fat you could loose your moobs within a year very easily with gym and the correct diet.
Any questions just ask.
Jake