Hello Benjamin,
if Rodovid (under whichever name) was to become a Wikimedia project, that would mean - It benefits from Wikimedia's fundraising drives - It is featured prominently on all of Wikimedia's portal pages - It becomes part of Wikimedia's press and publicity efforts - It becomes as integral to the thinking about external partnerships as other projects - It is maintained, to a certain extent, by our paid and volunteer administrators and developers...
..and so forth. There is always the concern that new projects distract from improving existing ones. For each of our projects, including Wikipedia, there are huge wishlists of software changes, community processes, surveys, partnerships, and so on -- we need to make sure that we grow at a manageable rate.
So, from the point of view of the Foundation, accepting a new project is quite a big deal. That's why the processes to do so are rather complex. Part of the process is a community poll about whether the project should be launched within Wikimedia. Our process does not yet deal with "adopting" existing projects (this has never been done), but you could start a slightly modified poll, similar to the one at [[m:Wikinews/Vote]], and probably get away with it.
Essential for your success is that you can generate not just a solid majority in support, but also excitement in the community about the idea. Such excitement was clearly visible with Wikinews and Wikiversity; I am skeptical if there is similarly broad interest in genealogical data in an experimental wiki environment. I know there are a lot of enthusiasts, of course.
Even though the idea of a "World Family Tree" has some appeal, I am also not convinced that this is an experiment that needs to be taken up by the Wikimedia Foundation; given the primary mission to bring knowledge to human beings, it is natural for the organization to focus on applicable and practical knowledge. (Hence projects like Wikibooks, with its strong focus on learning materials, and Wikiversity, with its learning and research angle.)
However, do not let this discourage you; if you truly want this to become a Wikimedia project, do campaign in the community for support. Only when such support is visible do I expect that the Board might get behind the project proposal in a big way. As a personal suggestion, I recommend changing the name before campaigning; something starting with "Wiki-" and reflecting the ambitious nature of your goals (such as "Wikiplanet", but that one is taken) might work better.
Erik (not speaking for the Foundation, of course)