I don't think it would be appropriate. Can you imagine sending out an invite to a team dinner and sharing your menu of excellent primal meals (nothing overtly "fatty", fairly healthy looking to CW standards), and having someone email back with information on how meat is bad for you? And how veganism will save the world? It would piss me off and not set the right tone.
You could, however, express concern over not appearing to have any alternatives for gluten-sensitive kids. Maybe no one has that problem on the team, so that would make it a harder case to push. To me, the first step is highlighting that not everyone has the same needs.