Alright here we go, Bommer you are wrong!
You can check your tank for stray voltage and it has nothing to do with induced or decoupled voltage. Stray voltage typically originates from bad insulation on a device such a pump which is in contact with the tank water. In the case of conductive salt water the potential for electric shock is high! Battery terminals with corrosion is the same effect as salt creep and can enter electrical devices such as lighting that may be sitting on top of the tank.
Everyone knows what will happen if you are in a tub of water and the hair dryer falls in. You will be zapped beyond belief! Why? Because you are becoming part of the circuit that is passing the electricity and the water is your conductor. That's why most municipalities have changed their construction codes, to state that all rooms containing sinks or tubs should have GFI protection on any outlets in a certain range of that sink or tub.
If you come into contact with one line at a time and you are not grounded, you will not be effected. Power line men do it all they time, in fact now, they are using helicopters more and more to actually suspend off of live wires they have energized themselves with. But surely if they where to touch ground, they would fry! If you touch one wire and you get shocked, you are grounded. You will not be shocked, if you are floating in air and not in contact with ground, but thats impossible for us, we are always grounded, some more than others.
Let's understand how breakers work shall we:
Breakers are rated to not allow a maximum of amperage (current) to flow. If a breaker is rated for 10 amps, then the breaker will cut the circuit if anything above 10 amps tries to pass. This has nothing to do with voltage! You could have 1 amp or 10 amps, it's still 110 volts, not 75. If you plug a drill into an outlet it will still be 110 volts no matter what, but it may draw 12 amps of current, which would pop the 10 amp breaker in no time. The only good a breaker is to a tank, is if you are drawing more current than the breaker will permit. It's never a good idea to change out a breaker with a higher rated breaker, because the wires in your walls may not be rated to handle the current increase and could cause a short circuit.
When a short circuit happens the potential for the maximum amount of amperage to pass will occur; this amount is only limited by the wires ability to carry the current as well as how much current is being fed to the circuit itself. Without a fuse or breaker, the current would continue down the line, the wires would heat up until they melt apart and or a fire breaks out in the house.
GFI's are ground fault operated, meaning they detect the pressence of electrical current attempting to pass the grounding part of the plug. If current is detected, then the breaker will cut power.
Most pumps, heaters or any other device that only has a two pronged plug are not grounded. A device that is in direct contact with the water, that is not grounded should be grounded by the use of a grounding probe! The grounding probe runs directly to the GFI plug-in outlet and should be plugged in only to the GFI outlet, not a power strip! A grounding probe plugged into a non grounded power strip is worthless, even though the power-strip is advertised as grounded, never take the chance! Always go to the GFI outlet!
No one should ever assume that just because they can stick their hand in the tank and not get shocked, that it will never happen. No one should ever run a tank unless they are absolutely certain that all devices are grounded.
Now you may be saying, I have a grounding probe and I don't have GFI protection and I don't get shocked anymore. That's because the outlet you have the grounding probe plugged into, is itself grounded. If you look outside your house (usually near the telephone or TV cable line) you will find your grounding rod, thats where the stray voltage is going, into the earth ground. Don't let this lead you into a false sense of security though. You still have a problem in your tank and you should find out why you have stray voltage.
To check your tank for stray voltage, you need a multimeter, set to 110 volts or higher on the AC scale. You will attach the negative probe of the meter to the grounding probe or any other ground, like the screw that holds the plate onto the outlet (if its not painted or if you scratch the paint off it) or if you are skilled enough to use the ground on the outlet itself. Do not to touch the metal parts of the probes with your fingers. Then use the positive probe of the meter to test the tank water. If you see any sign of voltage, your tank is energized and passing current to the ground, you should find out why and what is causing it by unplugging each electrical device one by one till the stray voltage is gone. Once the meter falls to zero you will know what is causing it.
When the stray voltage has been eliminated then the current will not be passing through your tank. Your grounding probe in your tank will then protect you by tripping your GFI protection. This will could possibly save your life but will shut down your tank.
So, whether or not you decide to put in a GFI outlet or not is up to you. If your tank shuts down while you are not at home because your GFI tripped, are you going to be cool with that?
It's your choice, let the current go to ground and hope you do not ever become a greater ground than your earth ground or put in a GFI and deal with the tank going down and possibly saving your life.