Say I have a page page.example.com/page. In my (python) server, you only get served html if you are logged in, which you can do at page.example.com/login. If you aren't logged in, the server responds with a 404 error.
Does this mean that web-crawlers would be unable to index this page? Or, more accurately, they wouldn't index it, because it "doesn't exist".
When Googlebot see 404 HTTP status code then they don't index that page at all. It will even remove the indexed pages if they continue to see 404 status for a long time. So hope you understand how Google seriously see 404 status code.
You should add functionality like quora, they allowed to view n number of pages before they force user to logged in. Google called it first click free, but now it's called flexible sampling
