Answer: yes it does, and a lot!
Here is both lens- and body-stabilization turned on:
... And here is only body-stabilization turned on:
... Here is only lens-stabilization turned on:
(This is the sharper of two, the other looked like the middle pic)
These are hardly conclusive, since these things vary from second to second. (It's always a good idea when using dicey shutter-times to takes several pics at once, preferably in serial-shooting mode.) But it's clear that having both turned on is a bad idea.
Below: cameras can look funny when fitted with a lens of a different size-ideal. :-)