Can a lead acid battery charger and the battery be used as a UPS?
This sounds like it will work, but there may be some pitfalls. First, ensure the devices are very flexible in their input voltage, lead-acid batteries can vary a bit in their voltage. Put a voltage regulator in between if you're not sure. Second issue from the top of my head could be that the charger puts a load on the battery when turned off, but the auto-cutoff makes this unlikely. This could be fixed with a heavy diode.