No. Social media is only increasing the gaps between people. “Fake news” is the best example of the manifestation of Culture as groups of people believe what is more comfortable to them, regardless of how far fetched that is.
Social media, indeed helps to interconnect the various groups of people, drive global awareness, and give a voice to collective human needs that were suppressed so far, but social media does not drive people closer together, at least not by default, and definitely not without wise intervention.