No, Italian-Americans should not take offense to their depiction on The Sopranos. It could be argued that, if they took offense to The Sopranos, they should also take offense to movies such as The Godfather Trilogy and Scarface. The truth is that some Italian-Americans do act this way, and at no point in The Sopranos do they say that all Italian-Americans act this way. The show depics the life of one Italian-American family, not all.
I don't think there is any real reason for Italian Americans to be offended by what happened in The Sopranos. The majority of Italian Americans are not involved in organized crime, or any kind of crime whatsoever. But aside from the that, showing the home life and family dynamics, it wasn't too far off the mark.
The Sopranos was a very successful TV show that millions of Americans tuned in to watch. I do not believe Italian-Americans should take offense at the depiction of the Italian-American community. These types of depictions have been happening in film and TV shows for more than a few decades. It wouldn't seem fitting to be offended all of a sudden.
Its just TV,they should be more worried about the way they are depicted in the Jersey Shore. The issues those people pushed on the country, allowed the masses to think that Italian Americans are just up to no good. The Sopranos was a classic as the Jersey Shore was a giant leap in the wrong direction.
People should remember that the show is just a television program designed for creating drama and excitement for the viewers, I don't think anyone should take a television seriously enough that they get offended by the depiction of an entire nationality of people, I highly doubt the producers of The Sopranos intended to offend the Italian-American community.