Does re-publishing viral content in reddit which is already been popular in other channels can help to drive traffic? I mean if I publish the content gathered from the internet which have got social attention and feature the url in reddit.
No, its not a good idea. First of all copying and publishing content gathered from other sites will get you red flagged from the search engines and also not to mention reddit will also do the same.
Instead of re-publishing the old article why don't you just rewrite it in your own way and add some valued extra information with it and than publish it on reddit.