Republics are not the opposite of democracies. A Republic is a nation which has no king. A democracy is something that is decided majorly by the people, with elected representatives representing the masses. The Internet actually does represent both a republic and democracy. Internet has no "Ruler" (no one Invented the Internet), and its content is determined by the masses. Democracy is shown obviously through the Internet by giving people a voice and the ability to vote (this site is a perfect example). The Internet, at least as it is used in American, reflects our affinity for democracy and the ideals of our Republic.
Yes, the internet definitely encourages democracy. The internet is a place where people can express themselves as individuals without the threat of being judged. It is also a place where they can find like-minded individuals. With that being said, the internet can help people find their voice as it has in other countries that are not democratic. I believe that is why certain countries ban the internet or websites outside their countries so that citizens do not cling on to those ideas and try to change other citizen's ways of thinking against their current government.
I think that the internet does in fact encourage democracy, because the free flow of information helps people communicate, organize and disseminate a wide range of information. The internet, primarily social media websites, were instrumental in recent pushes around the world to overthrow oppressive governments in favor of democracies, such as in Syria and Egypt.
What it encourages is a republic. A democracy means the majority can rule over the minority, a republic is the antithesis of such a thing and exists to protect the rights of the minority. This is what the internet encourages.....a freedom of expression, of thought and of acts that a democracy does not allow for, and consequently why the majority wants to control it unable to rule over us in that realm as they can everywhere else.
So no I do not believe the internet encourages democracy at all, it encourages the absolute opposite, and what America SHOULD be.