Well I've done it to 2 different family addresses here in the UK, and there is no invoice. But I keep choosing the gift option for my orders just in case they do it for some, and cba for others. But now I might have to try differently because some bastard just left this feedback, even though it's positive, it's rather annoying, and will show up in my feedback widget as well, which I won't be able to do anything about it until I get another 5 feedback to push it off.
This is the positive feedback they left: Item came direct from Amazon as a gift was a little confused at first.
As if that's positive, a-hole.