Scenario 1. Hot line to water via submerged equipment. This is when a submerged piece of equipment like a powerhead, heater or UV lamp fails and the hot line of the power supply gets in contact with the water:
a) No GFCI and No Ground Probe.
As the tank is isolated from ground via plastic piping and wood stands the water becomes energized to 110 V but the main breaker does not trip as there is no current to ground. Fish has no problem because they are in a situation similar to a bird standing on a power line. This is a VERY DANGEROUS situation for the aquarist because as soon as you touch the water you get electrocuted as you become the path of current to ground. Breaker does not trip as there is not enough time for it to act or enough current to create enough heat. (They are slow trippers)
b) GFCI installed but no Ground Probe: Again nothing happen initially but the tank gets energized to 110 volts. as soon as you touch the water the GFCI will trip within 5 milliseconds and below a current of less than 5 milliamps. You may feel a small shock but nothing enough to hurt. This is the safest situation for the tank critters but may still hurt the aquarist mainly if the GFCI is malfunctioning.
c) GROUND PROBE INSTALLED BUT NO GFCI (Our case of discussion in this thread): As soon as the device fails and a short circuit is established then current is established to the ground probe, current may or may not be high enough to trip the breaker. Fish and critters will die and corals will RTN. If the breaker does not trip (Which is most of the cases) the short circuit may not be noticeable and you will be at a loss of why your critters are dying, even if you touch the water you may not notice unless the ground probe is not making a good ground. (See also Scenario 3c below) This is also a dangerous situation for potential fire. The current could be high but not high enough to trip the breaker, wires heat up, insulation melts and they catch fire.
d) Ground Probe Installed and GFCI installed: As soon as the short circuit is established the GFCI will trip shutting down whatever equipment is connected giving you a physical indication there is a short and something bad for you to fix immediately. This is the safest situation for the aquarist but has the downside that if you are away from the tank for a long time the lack of operating vital equipment may put your critters at risk.
So under this scenario the safest for the aquarist is to use both a GFCI and a ground probe. The next safest is to use GFCI alone.