Political correctness is censorship, no ifs, ands, or buts. We've seen what's happened to societies with censorship, and those societies become places of fear, where people are too scared to share their wn opinions. In fact, political correctness even makes some people afraid to share their opinions in the modern day and age. Just say anything sightly politically incorrect and at least one person will attack it because it hurts their feelings. This country was founded on the right to say anything you want to without being persecuted, and if we let our current Thought Police take over, that right will be stripped away and we will be left with nothing.
No, society would not be more peaceful if everyone was politically correct, because we would constantly on edge. At some point, a person needs to speak the truth, because we can't be always afraid of offending someone. A person who tries to please everyone ends up in the end pleasing no one.
Being completely, strictly politically correct does not keep everyone peaceful. If anything, it just becomes a thin veil over people's true thoughts that creates a society of people who are never quite honest with one another. This is a recipe for disaster, since everyone would be terrified of slipping up and saying something wrong.
I do not think politically correctness makes for a peaceful world. What I have seen from political correctness is that people try to find things to take offense to anyway, or they continue to take offense to things in the past. One of the most annoying is the whole white privilege thing.
In popular conversation, the term "politically correct" is usually seen as a fault among those on the left, or progressives. The term itself belies definition and is usually merely held up as a kind of "boogie man" by the right. Since there is no clear definition of the term, there can be no clear result regarding a more peaceful society if everyone were "politically correct."