I think if you're on the internet all the time doing pointless crap like trolling, chatting and just doing time wasting games that wouldn't help your mind at all. If you're actively learning about something, researching, reading the news, having discussions etc I can see how that would help your mind. I like the internet for all of it's easy access to information and what's going on in the world and reaching out to other people from different places but I think that it can be a distraction from real life.
But I do think if you spend your real life time doing all the researching, reading books, discussing things face to face, going places, thinking etc, that could make you more intelligent too. And better rounded.