Little doubt about amplifier current requirement and THD + N
The efficiency of the chip means that if your speakers are producing 3 watts (6 watt in total), the power taken by the chip from 5 volts is going to be maybe 7 watts. That's an efficiency of about 86%.

The data sheet says "Efficiency up to 90%" so expect somewhere around 85% I'd say but it is not clear cut how accurate this figure is.

With 7 watts from a 5 volt supply, the dc current is 1.4 amps and if you have used a boost regulator to give you 5 volts from (say) 3.7 volts, the current from the battery will be at least 2.1 amps given the efficiency of the booster that I assumed to be 90%.

Regards THD read it this way.... the device can provide more power to the speakers but the distortion will be greater because the chip is getting close to its overload condition. Selecting the THD figures isn't really appropriate - if the distortion appears to high to the ear then back-off the signal fed to the device so it doesn't distort.