Having had sites of mine get to the top of HN multiple times, it's always been around 4 visits per second. (= 15K/hr, or ~100K total over the course of a story.)
Given that things like grabbing something from the database or serving up an image are on the order of a handful of milliseconds... it should be fine.
If HN were sending 1,000 visits per second it would be a totally different story. But it's not. The amount of traffic just isn't that much.
If you have slow internet or a very asymmetrical link, and the site is heavy (lots of pictures or other BS), then does the server just refuse new connections when it saturates the link? I'm not sure what the behavior is.
That won't be noticeable till you have 4 users per second hitting it...