Hi,
Ordinarily,it will work. However, car batteries are not deep cycle batteries and the computer ups is designed to run on deep cycle battery.
Batteries that aren't meant for deep discharge will sulphate if they are deep discharged even once. Once they've begun to sulphate, it only gets worse.
A "12 volt" battery at 12 volts is quite low as fully charged they should be at about 13.8 volts. The UPS is gonna check the voltage to determine when the battery is getting discharged by checking the voltage. So although you have a higher capacity battery that could maintain current for longer at the lower voltage, the UPS will decided when the battery is nearly discharged and it's no longer safe to continue.It will then turn off.
Cheers.