Oops, I somehow only saw Chen, and not the practical part. Yep, you're right, it's not folded.
You're also right about practical application. If you're planning on going after intruders with your katana (don't, you'll go to jail for a LONG time), it doesn't matter whether it's folded or not as long as it's properly forged - it's unlikely the burglar will be wearing armor or will have a sword of his own to parry yours with. Necks are soft