I used to live in Verona, Italy. We were there for 3 years in the late 1990s. The short answer is that the country is deserted during August, but it would affect people who live there more than it would affect you as a tourist. The small mom-and-pop type of stores and restaurants are usually closed for at least a couple of weeks during the month. There were always alternatives available.
If it were my choice, I would rather go in July, but that is mostly due to the heat. It can get unbearable there and there are still a lot of places that do not have air conditioning.