Recently we have seen a situation in which the entire internet in a country went down, and immediately everyone else in the world knew it. Social media allows people to connect across many boundaries, and there has been a rise in people who are very communication savvy. Even before the rise of social media, people had means of getting information across borders, and they will continue to do that using whatever social media and other means that they can. I truly don't know if the government can suppress information by controlling social media sites themselves, but I would think not.
As long as people have unfettered access to the internet and all its facets it is impossible to suppress the truth. Internet has become Pandora's box in a way, people have access to infinite knowledge unlike ever before. If the government makes a move to inhibit this technology people will staunchly oppose it. This is because people in first world mindset no longer view internet access as a privilege, they now view it as a right.
The government will still be able to suppress information, they always will be able to do so. There is some information that does not even gain enough footing to be acknowledged in social media, anyway. It will certainly become much more difficult for them to do so, however, due to the large amount of people using social media.
They can always pressure companies to take down certain information that they don't want, and they can always simply cut off the ability of people to use the Internet and their phones.
They can threaten or kill people who they think know too much or who they think are talking too much. They can create situations to discredit anybody who says anything that they don't want said.
Besides all that, they can always use social media as a weapon to introduce contradictory information and label anybody who doesn't believe the official story as mentally ill.