but can become live under fault conditions'
A metal bath meets those criteria for being conductive and not part of the electrical installation, but it cannot introduce any potential, as it's just a free standing object.
In the event of a fault could an un-bonded bath become Live ?
In some circumstances it could, spilt bath water around the bath legs that also reaches electrical equipment such as ceiling roses for the room under the bathroom is not considered as a fault in the electrical installation. It might not be a fault as such but the results cannot be ignored simply because that situation is not on the list of things that are "acceptable" as being a fault in the electrical installation.
Some people do stupid things, An example was a mobile phone on charge while being used by a person in the bath that was not bonded ( or earthed ) Charger fell into bath. Bath water and bath pulled up to about 115 volts ( mid way between Neutral and Live ). Everything in the bath and the bath itself is equipotential at 115 volts so the person is not at risk of shock while laying the water. Not until they are getting out of the bath and touching something that does have a path for current to ground.
DO NOT ATTEMPT TO VERIFY THIS