I posted the bits I think are significant below. Basically you've got the process right, but there is the possibility of some 3rd party components giving you grief such as a document manager. The biggest thing you're going to run into is the problem with Google being mapped to urls that are no longer available.
You can use 301 redirects to make sure humans get to the right location, but the spiders may not be totally happy which can result in broken links in search engines. Not a huge deal to some people. but usually is for someone going to the trouble of using SEF links.
My experience moving Joomla up from a subdirectory was almost painless for 5 different domains, and I didn't have to trust my shell skills with what I thought of as a critical operation. Obviously it's really important to make some backups since nothing is guaranteed.
Even though it might make a system operator cringe, I performed a drag and drop operation using my ftp program. Then I removed the subdirectory reference from my .htaccess and configuration.php files before uploading them, and browsed to the root directory of my domain. Success!! By the last site, the entire operation took about 2 minutes to complete.
I've still got some issues with Google trying to index pages from the old directory, and have had some difficulty in getting the things correct so that the spider doesn't give me errors. The site works fine though. If you can perform these steps, you can manually upgrade Joomla. I don't always trust automatic updates, even though it's probably just a script executing a file copy.
Since I use Firefox, I figured I'd look into some of the available extensions for it. FireFTP is a pretty capable plugin, and I verified that it supports drag and drop operations like I described. While it supports file resuming, it appears to have the glaring oversite of no functional file queueing system. It's available on the Mozilla site https://addons.mozilla.org/firefox/684/, and here's the plugin home page: http://fireftp.mozdev.org