Yes it has an impact. The two most important things are getting enough carbs to muscles, and eating the right number of calories.
Eating generally "healthy" foods helps with both of these things. When carbs are in beans, fruits, vegetables, and whole grains, they tend to have a lower glycemic index than in sugar and processed grains, meaning carbs from beans get absorbed into your bloodstream more slowly, so more of it can trickle into your muscles. If you eat a bunch of white bread, it will go into your blood too fast, and your muscles won't absorb it fast enough, and some of it will turn into fat.
Also eating healthy foods helps you naturally regulate calorie intake. For example, this weekend, I ate a box of oreos as a snack! 2000 extra calories which surely went to fat, with little nutrition. If I tried to eat 2000 calories of dried fruit I would have felt full and bloated after 600 calories of them.