The UPS batteries are usually China's cheapest AGM's, and the UPS chargers are simple low current single voltage compromises, designed to hold the battery full.
That is different that what the battery would desire, if/When it is deeply discharged.
These same batteries are also used in Lead acid jumper packs, ansd these also employ the single voltage low amperage wall wart transformer/chargers.
When Jumper packs are depleted the batteries within would be much happier if they were given ~ 30% of their capacity in charging amperage until voltage rises to 14.5 to 14.9v, and then that voltage held until the amps required to maintain it taper to 0.5% of the battery capacity.
Obviously this requires special equipment and some measuring tools other than just a voltmeter, so they would never recommend this.
As far as maintaining a UPS battery, Well, perhaps a deeper cycle and a higher amp recharge every once and a while applied every so often would be better than the UPS holding it at 13.6v always.
I deeply Cycle a Northstar AGM battery often, and I know that when i do float it for days on end, then cycle it, the voltage it holds during discharge is not as good as the day after I high amp recharge it from a deeply depleted state.
This PDF says to limit charge current to 0.35C and voltage to 14.9 on the widely used UB12120:
http://powerupco.com/site/wp-content/files/Batteries/UPG/UB12120.pdf
0.35c on a 12Ah battery is 4.2 amps. So the upper end charging limits would be to charge this depleted battery at 4.2 amps until voltgae goes to 14.9v
This is much different than the 13.6v 1 to 1.5 amp charger supplied with Jumperpacks or UPS systems.
While it can be argued the 1.5 amps at 13.6v simply takes longer to recharge the battery to full, I can argue the depleted AGM battery prefers higher charge currents when deeply depleted, and the 'trickle' charge is always best mentality does not apply to AGM's.
If one is really worried about thir UPS battery will not give them enough time for a proper shutdown, Perhaps a deeper cycle with a higher amp recharge at the limits of the batteries specs would be good for it, as long as the discharge was done quickly and the higher amperage recharge applied immediately.
But how much improvement, if any, would be hard to measure outside a laboratory.
And applying 4.2 amps to a 12AH AGM until it hits 14.5 to 14.9v at 77F and holding that voltage until amps taper to 0.06amps, is well outside the capabilities of most everybody's tools.
But if the battery were to be deeply cycled regularly, and I was responsible for attaining maximum battery life, that is how I would insist it be recharged.
Also note, Odyssey batteries, Thin plate pure lead AGM batteries, while a different beast than a chinese made AGM, has a 'reconditioning' procedure where they recommend quickly draining the battery to 10 volts than applying a very large amperage charging source until 14.7v is reached, then amps taper to near Zero, then discharge again to 10.0 volts under a big load and recharge again at high rate.
http://www.odysseybattery.com/documents/ODYSSEY_Battery_Reconditioning_Charge_Procedure.pdf
Is this 'recovery' procedure applicable to a cheapo Asian AGM battery made for a UPS system?
Will it restore capacity and improve its lifespan and allow one to have more time to shut computer down properly?
Well I suspect so, but Without performing the tests myself will not outright say it will.
And besides it is a lot of effort, and if the goal is enough time to shut down the computer, then a battery replaced more often, or replaced with a larger capacity battery, well both are easier than removing the battery loading it until it hits 10 volts then recharging it at 0.35c until 14.5 to 14.9v is attained, then holding that voltage until amps taper to 0.5% of capacity.
But the maintenance minded Bitoger seeking to extend the life of their UPS's AGM battery, might enjoy the process and the warm and fuzzies it could possible give
