Does a low-quality UPS affect its battery life?
I do know that even the quite expensive ones (rack-mount 3kVA APC) tend to destroy batteries.

The reason UPSes kills batteries is that in an UPS you(or the manufacturer) prefers to have faster charging of the batteries than long lived batteries. In practice that means the the charger part of the UPS charges the battery with a higher voltage than the voltage a normal charger(build for "normal" use, that is something more like longevity)

At the few discharge cycles an UPS battery usually has, it should last way over 2 years (say 10 maybe?). The common type of batteries is UPSes is AGM or adsorbent glass mat. This type of battery survives a larger number of deep discharges than most flooded batteries and AGM also has the pro of being storeable in any position you like it to be at.