Hey @Isadora,
Thanks for reaching out.
To move the license from your staging site to your production site, the steps in that article you linked to are exactly right.
In regards to site functionality, no, the migration of licenses will not affect functionality in any way.
In fact, licenses never affect functionality to begin with! 🙂 You can leave your “staging” site unlicensed, for example, and the plugin will work entirely fine.
A license only signs up a domain name for support and updates, so it does not have any impact on actual plugin functionality.
Lots of folks who have a staging-site and then a separate production site will often leave the license on the production site, where they can update automatically and everything, and then on the staging site, they just manually do updates themselves by installing the latest versions of plugin files.
If you are interested in this, you can access the latest versions of plugin files any time by heading to this page → http://theeventscalendar.com/my-account/downloads
I hope this information helps!
Cheers,
George