Is there any way to import rigid bound character with its animation, from Maya to Unity?

In Maya 2014, I bound an IK skeleton to a character, animated it and exported it to FBX. However, while the FBX would load well back on Maya, there would be no animation on the model (other than random rotations on the root joint), when I import it to Unity.
Is rigid binding in Maya supported by Unity?
Thank you for any help!

Is rigid binding the same as just parenting an object to a bone? This has to be clarified so knowledge of Maya (behind the scenes) is important.

Assuming the answer is Yes - since the pieces rigidly bound to the bones are rigid - skinning can still be done on the pieces - just rigid skin weight one piece to each corresponding bone without any blend weighting and the mesh components will stay rigid.