Justice Ginsburg thinks she would be. Given that Sotomayor was born in the Bronx, I assume she means that Sotomayor would be the first Justice whose grew up in a primarily non-English speaking household.
I'm not sure about this biographical detail regarding Sotomayor, but I doubt she'd be the first. Justice Brandeis may be one earlier example. I'm not sure what language was primarily spoken in the Brandeis household, but I would guess German, based on the following information: Brandeis's parents were German-speaking immigrants; Brandeis attended a German-language elementary school, the "German and English Academy;" the school was co-founded by his father, suggesting that his father had great fondness for the German language and culture; and Brandeis spent two of his teenage years studying in Germany.
It's also possible that Arthur Goldberg's parents, immigrants from a shtetl in Ukraine, spoke Yiddish at home. I can't think of any other examples offhand, but that doesn't mean there aren't any.
UPDATE: After I posted this, I remembered that Justice Thomas's first language is Gullah, an Afro-English creole dialect. And a commenter points out that Felix Frankfurter's family didn't arrive in the U.S. from Vienna until Frankfurter was twelve years old.