So how do you prepare for avoiding this fate before creating a "Show HN" post?
In my experience, most folks just want to see what the fuss is about, not so much make an account and start using the app. So as long as your post-login experience can take a few users simultaneously, you should be fine.
So there's no impact on my servers.
For a product you will get a lot of people from HN reading the landing page but relatively few registrations.