The plugin will not be updated automatically but the user sees a OS specific dialog from the Creative Cloud Desktop App “Plugin updates available”. Similar to the dialog “App updates available”. He has to navigate to the “Marketplace” > “Manage plugins” and click manually on “Update” for the plugin. There is also a button “Update all plugins”.
In my experience, many users do not update to the new version. That’s why I also show a message directly in my plugins. I have a simple JSON file on a server with the current version numbers and check these.