No, pokemon from the shared box do not count towards the seen/owned in the Pokedex (this can be changed if it bothers you of course... )
Pokemon from the "ChooseStarter" component do count for the Pokedex though: for example, if you choose Fennekin and then use the mod to change it to Skorupi, your Pokedex will state that you never saw nor owned a Fennekin and that you saw and owned a Skorupi.
EDIT: Actually, it would make more sense if the pokemon in the shared box were marked as owned as well... ok, changed it so that the Pokedex gets updated with the mons in the shared box.
(If you're planning to use the "ChooseStarter" component, then make sure to save and reload after using it but before withdrawing your mons from the shared box - EDIT2 save/reload no longer needed)