It really depends on the power supply used in the charger. Some are simple step-down-then-rectify and others are switchmode power supplies. Almost all laptops, PCs and smart chargers have these switchmode power supplies in them.
Switchmode power supplies can handle a wide variety of input power, because of its immediate rectification of the input. This DC power is fed to a step-down transformer, which essentially gets a square wave that's been flattened and flipped into pure DC.
Other power supplies use the AC input to step down first, then rectify the output and either limit it (eg using zeners) or resist it and rely on the input range being within certain limits. These can cause problems with modified sine wave inverters because the transformers aren't going to oscillate smoothly, causing the output to fluctuate. That isn't going to help a battery charger that's trying to rely on a steady voltage! There's also a risk when using these supplies with small portable generators - in particular the cheap ones you can buy for <$100. I've got one that fluctuates its output from 170VAC to 330VAC until you put a 100W load on its output!
Switchmode power supplies can handle a wide variety of input power, because of its immediate rectification of the input. This DC power is fed to a step-down transformer, which essentially gets a square wave that's been flattened and flipped into pure DC.
Other power supplies use the AC input to step down first, then rectify the output and either limit it (eg using zeners) or resist it and rely on the input range being within certain limits. These can cause problems with modified sine wave inverters because the transformers aren't going to oscillate smoothly, causing the output to fluctuate. That isn't going to help a battery charger that's trying to rely on a steady voltage! There's also a risk when using these supplies with small portable generators - in particular the cheap ones you can buy for <$100. I've got one that fluctuates its output from 170VAC to 330VAC until you put a 100W load on its output!
