Yes, that should work, but I'd recommend using the UpgradeMODX extra. It's a lot easier and can be more reliable. It does exactly what the FAQ describes, but automatically so there's less chance of making a mistake.
I bite the bullet and went ahead with the method in FAQ (while you were writing your response) and it worked like a dream. I had the UpgradeMODX extra installed but it was not responding. It told my that I needed an upgrade and provided the list of upgrades with the latest version check. But when I clicked "begin upgrade" nothing happened.
Will try again next time I need to upgrade and see if its still not working
What version of UGM is showing in Package Manager (it should be 2.0.3). If you installed it under MODX 2.4.0 or less, you should probably uninstall and remove it then download and install it again. You might want to do that anyway. In either case, though, be sure to save your GitHub token somewhere safe (if you have one), because GitHub won't show it to you. If you lose it, you have to create a new one.
It is version 2.0.3-pl downloaded yesterday through modx package management on MODX 2.6.1
Good, that's the current version.