Can a shield propagate EMI?
In an ideal system, the shield will not radiate (or pick up) and EMI.  As soon as I see an ideal system we can break out the Campaign, as I haven't seen one yet in 25 years in this business.  

The floating (battery) ground has no real influence over the problem-- well, at least no more influence than anything else.

An important thing about shields is that there should normally be no current flowing on that shield.  Any current flowing will likely be radiated as EMI.  The mistake that many people make is that they connect SHIELD directly to a GND pin of the same connector.  That's not correct.  SHIELD of the cable should be connected to the the metal chassis of the box, and GND should be normally connected to the ground inside of the PCB it's talking to.  

I'll also note that EMI is a hugely difficult subject that is often more art than science.  This answer just barely touches the surface, as we don't have the time or space to give this a comprehensive answer.  But I suspect that you might not want the more detailed answer anyway.