People definitely do notice table manners, or more accurately, the lack thereof.
I was brought up to wait until everyone was served or until told to start earing. We always said grace before eating, so it was sort of understood that you could start after that. We had to ask to be excused and then brought our own plate to the kitchen. Eating with knife and fork or spoon was expected, and the table was set with placemats, napkins, etc for every meal.
For my own DCs, I taught them to use knife and fork the British/ Irish way and they learned the American style from exH. We set the table for dinner every day. We often served dinner family style, so when grace was said everyone started reaching for food and passing bowls. I helped the youngest. The DCs could ask to be excused once they had eaten enough, and brought their plate or bowl to the kitchen. After they left the table they had to go off to play quietly and not bother or distract those still eating.
There was absolutely no knife licking, nose picking, taking food from others, slurping, chewing with your mouth open, talking with food in your mouth, spitting out food, whining about what was served, or blowing bubbles in your drink.
I sometimes see kids who have absolutely no experience of eating a meal from a plate, at a table, occasionally. I suspect the lack of manners comes from kids eating separately from parents.