This is my preferred site for these kinds of questions.
So it's a legit process, but why does it need internet access? I haven't been able to find an answer to that. I have found a page claiming that yes, it really does need that access, but no explanation as to why, which pretty much sums up everything I find frustrating about this kind of research.
Here is another page that might be the answer: apparently it's the program that polls other servers, such as your mail provider and anything you subscribe to, and notifies you if there's anything new there. So if you want that to happen, yes, it will need to work through your firewall.