There are two interesting factors regarding eco-mode and battery life, which are battery wear and battery operating temperature. The transfers to inverter operation will typically cause momentary operation on battery, even if mains power is present and the battery charger is able to function. This means eco-mode operation will require a transfer to battery much more often than the same UPS operated in double conversion mode. This may be of no consequence if such events happen only once every few months, but may create unnecessary battery wear if these events happen multiple times per day.
This extra battery wear depends on the implementation of eco-mode, the local power quality, and the eco-mode settings. It may be difficult to predict battery wear in advance, so it needs to be established over time with real-world experience at a particular site. In principle, eco-mode is more efficient so the UPS creates less heat.
This could mean that batteries run cooler, and therefore last longer. However, the reality is that this effect cannot be assumed and the battery temperature will be strongly affected by the UPS design. For example, if the batteries receive cooling from the UPS fans and those fans are off in ecomode, then the batteries may actually operate at higher temperatures in eco-mode. If the batteries are in isolated cabinets from the UPS power electronics, then there may be no effect from eco-mode. Therefore, no general assumption of the affect on eco-mode on battery life is possible, and eco-mode impact on battery temperature must be established on a case by case basis.