Well, I suppose you could turn up naked on someone's birthday!
Seriously, no, as Murphy says, they are two completely different things in Italian. Costume adamitico means "naked". If you were to buy a new suit or dress for a birthday or some other occasion you'd say "un vestito nuovo" (dress) or "un completo nuovo" (suit).
EDIT: Thinking about it, in Campania they also say "come mamma ti ha fatto" (come mamma l'ha fatto) to mean stark naked. This might be a regional thing: there's a famous song in Neapolitan "Cumm' mammete t'ha fatt'", so this may well be the Italianised and therefore local version of that! Campani, ci siete?