Upgrading WP and plugin versions via Github

I’m working on a site that has an outdated version of WordPress and needs to be upgraded. This site does not have FTP and all uploads are done through Github.

I have upgraded WordPress and plugin versions before simply through the admin panel, but as there is no FTP on this site, it’s not possible to do it this way.

Is doing this via Github as simple as downloading the latest version of WP/latest version of the plugin, unzipping it, and copying the new files into the site directory, and then committing to Github? Or would this break the site? Is there a step in here I’m missing?

Thanks.