I have to agree and disagree also.... just to be contrary
I think back to my youth, I was a teen in the 80's living in Australia. The church's presence in society was minimal, and I quite literally would have had almost no chance to come across true Mormon history. Something like "No Man Knows My History" just didn't exist in my environment. Now I think about teens living in Australia today, and they have a wealth of information at their fingertips. Where I would have basically had to write to an American and ask them to purchase certain books and mail them to me in the past, now I can type a google query and get all the info I need. So I think the internet does have a huge impact.
Now, that said, the internet actually probably kept me IN the church for far longer than I would have been otherwise. I spent 10 years doubting, and trying to figure out what I believed, and during that time (I am ashamed to say) I was usually mollified by apologetics I would find on the web. They were rarely satisfying, but they were enough for me because I was scrambling for any thread to hold on to. I studiously avoided "anti-Mormon" sites, so the only discussions I would engage in were on the Mormon Apologetic sites. Those sites kept me in the church for a long time, way past where I might have stayed otherwise.
For me also I lost my faith in God before I lost faith in the church (I know that makes little sense). The internet really had little to do with that. What the internet did for me was provide support when I needed it, and validation that I was already on the right path.