Trouble with networking, how important is it?

So, I am reaching out to alumni on linkedIn and I just call and talk to them about their experience. But I am wondering how does this help with getting an interview? Also is this a good way to network? I will start to also email people on their work emails. Finally, how important is networking? I though that first rounds where screen by HR, but I am seeing people say that if no one recognizes your name you have no chance and others say that it only really helps when you get on the job. 

Legit asking for advice so no mean comments please.