High voltages may be present inside the TV, and eliminating ground does not make the electricity harmless in water.
When energized electrodes are applied to water, an electric field is created which extends far from the electrodes. Depending on the voltage, whether there's pulsing or AC, and current this can induce muscle contractions and make people and animals unable to leave the water, or maintain a safe posture above the water.
So, in short, no - a battery and inverter combination is not safe, and certainly not safer than a GFCI protection unit.
While a properly used GFCI will stop the current very quickly once a wire or electrical appliance drops into the water - it will only do so if the appliance doesn't have an isolated power supply. Most electronics, however, do have voltage converters that isolate internal power from the power line, which means it's possible for a partially submerged electronic device to create an electric field in the water without causing the GFCI to trip.
The only adequate solution is to mount the TV and all wiring in a permanent fashion so it cannot come into contact with the water, and to GFCI protect it. If the TV is mounted to the wall, for instance, and connected via a short cord to a GFCI outlet mounted high on the wall with a tamper evident cover and lock (to discourage others plugging in extension cords which could reach to the water) then you'll achieve a reasonable level of safety. You may need a larger TV to make up for the distance from the water, and you may need more weather proofing if this is outdoors.
Any solution where it's possible for the electronics or wires to come into contact with the water is inadequate, regardless of the care of those using the equipment, or the protections you might put in line.
An alternative is using a tablet in a waterproof case, or one of the many newer waterproof or rugged tablets. It will probably be cheaper and more flexible than the TV, and if you have cable or satellite service you can use it with online streaming to get essentially the same content without having to use a real TV. If you already have a suitable tablet, the waterproof case would be cheaper than hiring an electrician to mount the TV and wire in a GFCI outlet.