Most FLOSS projects probably could benefit from the structure and services that a NPO could provide. However, whether or not you need to start your own NPO to gain these services is a different question. We'll try to address both issues in this document.
FLOSS Foundations spawned off a software project (of sorts). If you are interested in software systems to help in the management of non-profit organizations, join the Foundations Software list. The FSF Wiki on non-profit management software may also be of interest.