it depends on what type of UPS you are talking about ( power level ) and what option can you select for the battery charging. Boost charging might be a problem for several types of lead acid batteries causing cracking the case and the leakage of the battery due excessive gasing.
In small one phase UPS as an emergency you can theoretically connect car batteries but the problem is that the car battery is designed to give high discharge current during very short time ( start up of the vehicle ) and it i not suitable for deep discharge and frequent cycling so you would "kill" the car battery very quickly in UPS application.
As mentioned by itsmoked due safety but especially to save your many in the long time horizont you should use deep discharge batteries.
Most often you can find in battery datasheet if it is suitable or not for UPS application or you can contact your battery supplier what is his recommended type for UPSs.
