Obviously, the current draw by the application's circuit must be less than the maximum current output of the charger.
Otherwise, there won't be any current left over to recharge the battery.
Also, the application's circuit must be able to accept the full voltage range of the charger.
For instance, at room temperature the battery voltage can reach 15V (for a 12V system)
At very cold temperatures, the voltage can be higher.
Consult the individual charger's electrical data sheet for more details.
A very important aspect to consider is how deep the battery discharge is likely to be during a power outage.
A 12V battery should not be allowed to discharge below 10.8V (open circuit voltage).
Much below this voltage and the battery starts to deteriorate.
If the battery is allowed to go totally "flat", it's Ah rating will be greatly reduced or the battery may fail completely.
Using a charger that automatically disconnects the battery at the 10.8V level costs a bit more.
However, it may pay for its extra cost the first time it disconnects a battery that has discharged to a too-low voltage.
The Ibex L12BD-1.5/115AC charger is an example.
The recharge time for the battery will be a function of the battery's Ah rating and the amount of charging current left over by the application's circuit.
Another application note discusses battery charging time.
The next figure shows a possible way to connect both a charger and a power supply to a load.
This allows the use of a small charger whose only responsibility is to maintain the charge of the battery.
The power supply is used to power the load while the main AC power is on.
This method can be less expensive than using a large charger when powering a large load.
There is, however, one caveat with this method.
The power supply voltage must be as high, or higher than, the highest battery charger output voltage.
At room temperatures and above, the charger's voltage will be 15V or less (12V system).
At -40C the voltage may be as high as 16V.
If the power supply's voltage is too low, the load may clamp the charger's output at too low a voltage to sufficiently charge the battery.
The rectifier in series with the power supply may be omitted if the reverse current drawn by the supply (from the battery) is at an acceptable level.
It's recommended that schottky rectifiers be used, as they have a much lower voltage drop than standard rectifiers.