Shouldn't be a problem as a lot of the gravestones up here have had that done, but they normally leave them up against the walls or laid down at one end of the churchyard.
Personally i dont think they have the right, when you get buried you buy that plot, and they shouldn't be moved, the history that gets lost - Look at Whitehaven George Washingtons grandmother's grave got lost 'cos they moved all the headstones, and they said all the remains were re-intured -- where at no-one knows.
Gravestones are records just as important any other records in a library
Anyway we'll see
Andrew