Electrically it'll work, but mechanically it'll suck. Right now you hold the phone in one hand and swipe the card with the other. With this adapter, you'd need three hands: phone, reader, card. Or find a place to put the phone down while you run the operation.

For something like a card reader, you really want a device that plugs straight into the phone. If Square isn't able to build a Lightning reader just because Apple controls the port, that would be kind of irritating.