I think it depends on what is inside the shower head and how its wired.
The two lines from the power plug must go to a heating element. If the ground wire is not connected
then all of the current from the hot wire must return to the neutral - no other path.
If the ground is connected to the metal shower head, then some of the current may leak through the shower head to ground.
If the tub is metal and is grounded, then, assuming a path through the water, some of the current may leak that way.
(because the water from the shower head breaks into drops, the current path is broken - it isn't so clear when a body is in the shower
as that creates thin layers of water on the body and could allow a current path)
If the metal shower head and the metal tub are both grounded, I would not expect much of anything.
Not interested in testing this arrangement by taking a shower.
Note that electric "instant hot" water works in a similar manner, although in US, there are various
plumbing and electrical codes involved for safety.