Auto Vertex Painting
Will it work on multiple objects at the same time and keep vertex colors per material consistent between them?
Yes, it works for all separated meshes and keep it consistent. One Vertex ID (Color) is generated for each material, if faces of different meshes use the same material, they will have the same Vertex ID (Color) assign to them.
How I make the add-on ignore some meshes?
Hide the meshes you want the add-on to ignore (the eye icon). All meshes not visible in the 3D viewport will be ignored by Auto Vertex Painting.
What happens if the mesh face has no material applied?
The Auto Vertex Painting add-on will generate a unique vertex color ID to "no material". All the faces, with no material applied, will be paint with this color ID.