There's no real way of knowing where she was born - and since obviously she was never given a SSN or birth certificate, as far as the government is concerned it doesn't really matter - but it's hard to imagine Babs didn't fake her into the federal databanks once she took her in, so effectively yes. Certainly yes if the adoption bullshit from the recent mini is canon.
And now I'm picturing former-Congresswoman-Babs trying to explain to utterly-indifferent-to-all-things-non-Bat Cass why it's important to register to vote.