Voltage used to charge a UPS-Inverter and its usage
Electricity isn't simply on or off... you're missing the quantity of electricity which is measured in Amperes (Amps for short).

So, while your UPS is charging, it's using lots of electricity to charge your UPS storing a large amount of power as well as the relativity small quantity of electricity powering your house.

When the power is switched off, your UPS is just providing the relativity small quantity of electricity for your home appliances.

So, in the space of time it takes to charge your UPS, your electric company will charge you the cost of 8 hours worth of electricity, plus 2 hours of normal use, plus a tiny bit extra for the inefficiency of your UPS.

If you do this, it will likely cost slightly more than you are paying now, due to the UPS inefficiencies.