The above does not mean you can ignore amp draw on your device.
With a parallel dual battery regulated MOD, with good 20A batteries, again no worries.
But if you have a single or series battery regulated MOD with a silly low ohm build (0.2 or less in power mode) then you need to watch that your single battery is not drawing too many amps at high power, with when in a lower voltage state.
DNA and Provari chip-sets will monitor for this and give 'weak battery' warnings, and limit the power to limit amp draw.
I guess the lower cost China mods should do this, but wouldn't guarantee it myself.