While minor updates rarely lead to breaking changes, simply updating isn’t enough. There might be some deprecated methods you’ll have to replace, you might want to update (or replace) some plugins, …
Long story short: you’ll always want to update locally, test it and make necessary changes before deploying your site to the server.
Thanks for your explanation. That makes sense. At the moment, I don’t have a proper local development environment that allows me to test locally. That’s why I use a subdomain that is not public for testing.