Even out here in the provinces, I doubt that most people drink anything before lunch, and probably drink water with lunch.
My own experience comes from small village life. In my ancestral village (pop. ~2,000) I only saw retired people and independent artisans. Both groups seemed to live for apéritif and wine with lunch. And any other village that we visited, it was the same thing. Plus there was always a pot of coffee on the stove, especially on cold days.
I'm sure that things have changed with the younger generations -- except when they visit their grandparents.
Italian barista will certainly make you a cappuccio after 11 (or 10, depends), but they will likely think you are philistine trash as well. If you must take coffee with milk later, order a macchiato. It carries no similar taboo.