Most protected cell batteries have that low of a cut-off - things like the cheaper trust-fires for example - if the battery manufacturer states that the battery can handle a high amperage load then you can take the chance.
The theoretical maximum of the device is
30 watts with a
1.2 ohm coil pulling
5 Amps at
6v but I think you'll find it hard to achieve that
the variable wattage mode will limit you to
15 watts which gives with the same
1.2 ohm coil approx
4.2 volts with
3.5 amps
I personally use AWR cells and the Panasonic hybrid Li-Ion cells that can handle a discharge current of 10A and have no problems.
Basically if your batteries are rated to be able to safely handle 5A loads without tripping then if you're comfortable with that give them a try - your biggest obstacle will be whether the stated manufacturers amp trip limit is factual or not