Is it possible to fully switch the installed language of Windows Server after installation?

According to a blog post by Raymond Chen titled How much gets localized in a localized version of Windows?:

Windows Vista mixed this up a bit by introducing Language Interface Packs, which are "mostly-localized" versions of Windows. Each Language Interface Pack starts with one of the "fully-localized" versions, and then re-translates a subset of the resources to suit the target language. Strings left untranslated receive the translation from the base language.

Which leads me to believe that, no, it is not possible to fully change the language of an installation, as the Language Packs only contain a subset of all material that is translated in a "normal", translated version.

Additionally, the Windows Language Interface Pack FAQ mentions:

The LIP packages do not have complete localization coverage. Only more frequently used UI is localized. Components not localized include administrative tools, system error messages, event logs, and others. Only the basic User Assistance (Help) files are localized.

If an Original Equipment Manufacturer (OEM) computer with LIP pre-installed is purchased, and the LIP language is selected at setup, the setup experience will be localized as well.

According to this link installing Multilingual User Interface Language changes whole operating system language, which will solve your issue.