Scarves, when attached, do not actually raise the stat of the Pokemon right away. According to Bulbapedia:
>They will boost the Pokémon's performance in the primary round of a Pokémon Contest, the Visual Competition of a Super Contest, and the Introduction Round of a Contest Spectacular.
This implies that only the performance of the Contest is raised, for their respective stat. So a Blue Scarf would increase performance in Beauty Contests, Red Scarf for Cool, and so on.
So technically, yes, it does go "over", but not in the same way you would expect it to.