You can test lead-acid batteries by measuring the resistance between the terminals. Most upses only look for voltage from the battery. This means that the battery casing can split open, leak acid, before the batter grounds out or goes kaboom, or whatnot. I had one battery in a 64 battery cabinet leak out and ground out the batteries.... The bloody APC Silcon (now discontinued) ups didn't throw an alarm at all, all we noticed that there were no lights all of a sudden when the power flickered. It was apparently a firmware bug or some sort because APC swapped out the firmware IC chips when they replaced the batteries.
Generally, with larger ups systems, you tend to have a quarterly battery inspection where a tech comes out, takes voltage and ohms readings for each battery in the unit, and visually inspects the batteries in the cabinet.