If the transformer is a electronic one and that your GFI is a type which can detect unbalanced DC as well as AC currents, then there is a possibility that it will trip.
I can't see any way the GFI could see the difference between a normal load and a "human" load. Like Pauluk said, the current on the secondary side will just go from one pole to the other. But then, there is a lot I don't know about electronic transformers.
I've seen that many new RCD/GFI:s are advertised as DC-sensing (class A), but I thought this meant rectified DC at mains voltage. (When there is no transformer, just a rectifier)
I think you are perfectly safe in a bath with 16V DC. (Here you are allowed to have cables for 30V ripple-free DC in the bath tub.) I'd be a lot more worried about a transformer on a wet bathroom floor.
[This message has been edited by C-H (edited 10-16-2002).]
