Standard convnets do not contain explicit rotational invariance (unless you include a layer such as this: arXiv:1506.02025v1). They can however learn rotational invariance if you feed them rotated images.
We did not train ImageIdentify to be invariant under arbitrarily large rotations. This is fairly easy to do: show the network couches rotated at all angles.
There are no sofa's in this list, the closest thing I can find is a "studio couch, day bed": http://imagenet.stanford.edu/synset?wnid=n04344873