No. The update files are always just the files that have been changed since the last update.  That's why it mentions the version numbers in the file name, for example "Renryuu Ascension 23.06.20 - Update files for version 23.05.25 or later only!" is the latest update files, and can only be used on version 23.05.25, not on older versions.
You can download the full game, and copy&paste the entire content of the www/save folder of the old game to the new game folder. Make sure to copy everything, as the loading screen won't show any save files without the .global file.