No. Only sufficiently creative works by humans have copyright. Some sort of QR code or barcode could have patent protection but never copyright. Trademark protection would be unlikely for something as generic as a QR code.
Nintendo once made a game system which only accepted floppy disks embossed with the Nintendo logo[1]. Which obviously can be protected by trademark law.
Perhaps they should use the camera to look for some pattern they can copyright.
Of course, for Nintendo I don't think it prevented piracy...
I doubt that a camera would be practical though, the slot for the pod would need to provide illumination and the camera lens would need to be positioned far enough away from the pod so that it could focus on the logo printed on top of it. The camera would need to be of a relatively high resolution, which would be expensive, otherwise competitors could print artwork which is not the trademarked logo but which does fool the machine into recognising it.
Perhaps they should use the camera to look for some pattern they can copyright.
Of course, for Nintendo I don't think it prevented piracy...
[1] http://www.glitterberri.com/developer-interviews/how-the-fam...