Hold on, if the floating is no risk, does it mean you can touch both the neutral and the earth without shocking even though they are 100V apart? Because there is no return path for the current?
I wouldn't say that is true.
https://en.wikipedia.org/wiki/Stray_voltage
Voltage (known as potential) means that there is a measurable difference in potential between two points.
As with everything in nature, these two points want to be at the same potential, so current will flow between them to bring them to the same potential
At above ±50v the potential is high enough to overcome the resistance of your body
The higher to potential, the more current can flow through your body and the more energy (joules) is transferred for a given time.
So the higher the potential, the quicker energy (jules) can flow from one point to another. The flow of that energy we measure in amps.
When it comes to shock and actual death the amount of energy (joules) is the most accurate measure of what is dangerous.
So even if you have a very high potential (volts), there will only flow as much energy as available (joules) at a given current (amps) before the two points reach the same potential.
Frequency also plays a role: 50/60Hz also happens to be the perfect frequency to cause your heart to lose its natural rhythm, therefore death by cardiac arrest is the most typical mode of death for mains electrocution. Whereas death by direct current will typically be due to joule heating (aka burning) and typically requires quite a bit more energy for you to die.
Keep in mind that if a multimeter measures a voltage between two points, there is some path that will allow these two points to reach the same potential if connected.
Last but not least, stray voltages can often be of low joule energy and therefore touching will bring them to the same potential without noticeable effect to the human because of the low amount of energy that passed through them.
In this diagram there is no return path in case of an earth fault on the circuits connected to the ups/inverter when Eskom is off and the load is supplied by the inverter. I think a better way of connecting the inverter is to connect the inverter mains input before the main E/L and to bond the neutral and earth on the inverter output and then run that through the secondary E/L. Connected in that way all the circuits supplied by the inverter will always be protected by the secondary E/L, whether Eskom is on and running straight through the inverter or Eskom is off and the inverter is supplying the load.
Again, you are creating a dangerous circuit. Your earth wire to the inverter becomes a parallel conductor back to the Eskom transformer.
Electricity takes the path of least resistance. By paralleling you decrease resistance. Therefore, this new magical bond you've created will mean your home neutral and earth are sharing the neutral current back to the transformer. Bonded by your inverter wire.
You are connecting a wire between earth and neutral, the fact that it runs all the way to your inverter just makes it more dangerous. (and it is in contravention to SANS I should point out)