The FOV will be different but the image is still at 12mm f/4, you are just taking a portion of it. So if something was out of focus it remains so, etc.
I was wondering when the Fov/Dof argument over crop mode would pop up. Reducing the sensor size reduces field of view. When you reduce the field of view you have to move away from the subject or use a wider lens to get the same frame. Depth of field is directly related to both focal length and distance from the subject. Less focal length = more depth of field. More distance between camera and subject = more depth of field. In fact there will be quite a bit more depth of field on crop mode for any given f number. f numbers shouldn't be compared over different formats though as they are only part of the bigger depth of field equation and it gets confusing.
Saying that, it doesn't mean to say we still can't get shallow though. Andy's frame show's just how good crop mode is and getting shallower for that shot wouldn't do anything for the background really. In fact it opens new lens choices for me, I'm quite excited about using wider lenses on anamorphic which would normally vignette like crazy, 35mm Flektogon for example. I'll post some results when I shoot them.
Crop mode is a great option but I think it's a bit unfair calling it crop. It's more like a change of sensor size to a different format. Should call it 2/3 mode or something.
I hope that wasn't patronizing. Arkanoid's great by the way but I think it ate all my battery power! Looking forward to testing dual iso!

Cheers