Let me take a stab at this, These are my opinions, (others - please correct me if I am wrong!!)
I think the answer to your question depends on the situation.
In a dwelling that has metal waterpipes used for or connected to the grounding electrode , are metal plumbing fixtue supply lines significantly safer than flexible plastic supply lines which are commonly installed.
First, a GFCI (if working) will help protect from harmful shocks.
Aside from that, (No or non-working GFCI) if you're talking about a live conductor making contact with the Sink, Tub, or Plumbing fixture itself the supply would have to be metallic to make the Breaker trip. I don't think that the water itself would permit enough current flow to trip a breaker.
(The current flow would depend upon the ammount and type of impurities in the water, as pure water is actually an insulator)
In a situation where you (a person) come into contact with a live wire or get some leakage and are touching the Sink, Tub, or plumbing Fixture, it would be a bad situation but probably be best for you if the supply connections were not metallic. But that might be different if you were actually in the Tub.
In short, after all this, I would have no recommendations except to install and test GFCI's on a regular basis and use common sense when it comes to 'water and electricity'