When you gain fat by over eating do you naturally gain muscle as well, and if so, what possibly is the fat gain to muscle gain ratio?

Not really: When you are not working your muscles your body preferentially stores extra food as fat not muscle. http://www.health.harvard.edu/exercise-and-fitness/7-tips-for-a-safe-and-successful-strength-training-program

No muscle gain: The only way to increase muscle mass is by resistance training for several hours a day 5-6 days a week for months to years. Otherwise the obesity epidemic would also be called the" strong man epidemic". We wish we could get stronger just by eating, but it is not possible!