Using two supplies in this way wont do anything that couldn't be done with a single power supply.
After a power failure, the voltage will sag due to the internal resistance of the battery, and as the battery discharges, so the voltage will not be very constant. What voltage are you really trying to maintain at the load?
13.5V will float a SLA battery (at room temperature), but will not recharge very well it after power is restored. That requires a much more complicated charger.