Regarding Dawkins, Intelligent Design, etc, it seems quite hopeless for LSV to want to enlist the Vatican for his position. When he mentioned ID here on the blog over the last several years, it has almost always been in the context of rejecting evolutionary biology. Using a disproven concept like irreducible complexity or with ignorant jargon terms from information theory, going on about impossibility for some of life's macromolecules to form through natural processes, etc.
When talking about ID in that meaning, as was his usual story, the Vatican could hardly reject his position more firmly. When it comes to the mechanics of life, their position is mostly one of theistic evolution, i.e. accepting Genesis as being metaphor or allegory rather than a real literal explanation, accepting an old earth and accepting the theory of evolution as the best, at present only viable explanation for how the diversity of life on earth came about during those billions of years.
As an example of how much at odds the Vatican position is to LSV's usual form of ID advocacy, here is a report on how far the acceptance of evolution has progressed since pope John Paul II's perhaps slightly more tentative 'more than just a theory' words, and how strongly people inside the Vatican reject ID: