It shouldnt ideally.
But on my machines i dont need to run it as root for it to work.
There are a few posts on other forums that you could try:
https://superuser.com/questions/564534/only-root-user-is-able-to-open-libreoffice
They more or less say the same thing. It looks like if you start libreoffice as root, it generates a config under the root user, then whenever it tries to load that config as a standard user, it fails (If your having the same problem).