I can only answer you from the perspective of being the child (back when dinosaurs roamed the earth). My father was an excellent cook. My mother was okay and learned from him. However, both of them had one thing that I've had the toughest time getting rid of. They both figured that if something tasted good, the next day it would taste even better on a big hunk of Italian Bread. And Dad would make special trips to the city just to get bags of Italian cold cuts and bread.
I could live my whole life and never have another baked sweet, or even candy, but the occasional slapping of something on to bread is my "20." Even a fried bologna and egg sandwich brings a smile to my face - not surprisingly, that was a breakfast of my youth.
So, IMHO, parents very much influence how their children will eat. It could go either way. If the cook in the home sucks and thinks catsup and marinara are interchangeable, the child might actually learn to cook and make better food. But if you learn to love Mom's meat loaf or Grandma's lasagna, you're probably still going to love them when you are an adult.
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine