Well, to be pedantic, this will upgrade a 'clean' 2.4 to 2.5. If you have changed anything or added any optional plugins then it's somewhat more complicated.
Personally - I would *still* follow the upgrade instructions. Copy (or move or whatever) the old Moodle code out of the way and replace it with the new (you can probably copy it and basically do the above). Then replace any plugins with updated versions.