That will work, Monty, but let's take a look at how long it will last...
***WARNING*** Math is involved :becky:
The FEC draws approx 400W when the ignitor is on and about 50W after that. At 12V (the battery operating voltage), 50W is 50/12 = 4.2amps. The battery pack that you linked has a capacity of 28 amp hours, so ideally it will last 28/4.2 = 6.6 hours, but realistically you won't get that out if it. At some point the voltage will drop too low.
I use a marine battery with 100AH capacity and an inverter/charger with an automatic transfer switch. When the AC power is on it send that to the FEC and charge the battery but when the AC power fails it automatically switches to the inverter and battery. With the 100AH battery it will last about 20 hours if needed.