Yes, it can. But you will need to change a setting in the "Modify Links Options" page.
The Modify Links process has a safety feature that keeps LinkFixer Advanced from writing broken links in the event that one of your rename rules has a typographical or other error. By default, LinkFixer Advanced checks to be sure a child file exists at the location specified by the "To:" field of the rename rule. If the path that would be created by the new modified link does not actually point to a valid location that contains a child file with the correct name, then LinkFixer Advanced will usually not modify the link (as it would be invalid from the outset).
The same safety mechanism causes LinkFixer Advanced to balk if the child file is password protected.
This safety setting can be disabled. On the "Modify Links Options" page, un-check the Expert Option that says "Only modify links if the child file can be found". This will allow LinkFixer Advanced to modify links that point to password protected child files.
If this safety feature is disabled, you will need to be extra careful to be sure that your rename rules are correct. With this safety off, LinkFixer Advanced will modify your links to point to any location you specify -- even if that location does not contain a child file.