It's not that simple
First of all, converting those 3,5ish volts up to 12 volts which is used by mainboards isn't simple.
If you want to combine your PSU and your battery backup, do it the Google way and use a 24-ish volt intermediate stage with 2 12V lead acid batteries. The first stage converts the 230 volts to roughly to 24-28 volts to charge the battery, while the second stage converts those to the voltage the rest of the computer needs.
Biting the hand that feeds IT
