Yep, this is how it works.
Of course you should make a backup in case anything goes wrong (so far I never had problems, but things can happen). Both for the database as well as the file structure.
Save any custom themes, etc (which should be in the "uploads" folder anyway, but better save than sorry).
Important to not delete the files/folders mentioned on the manual page.
I personally rather set up a new instance, but usually there aren't that many surveys and users to "transfer" for me.
If you can't afford downtime, I would create a copy of your current installation and run a test update and see if everything goes well on your server, or if it breaks something. Once this is done, you can update the main installation. It is not necessary, but if you run a lot of studies, it is probably worth the extra time just to make sure you are safe.
I answer at the LimeSurvey forum in my spare time, I'm not a LimeSurvey GmbH employee.
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