I think it depends on how you mean that. One way to imagine the phrase is to think about people with cloistered views in politics, religion, social views, etc. These people could get "offended" by being exposed to more cosmopolitan views but ultimately evolve to be better people by the experience - either by coming to better understand their own positions or by updating their beliefs to reflect things they have learned.

Another way to be offended though is just for jerks to say horrible things to you. Maybe that could be beneficial in terms of developing tougher skin or something, but it seems like that should at least be an optional thing. You might get tougher skin if I rubbed you with sandpaper for twenty minutes a day - but I should probably get your permission first.