A battery will be CHARGED if you apply a higher outside voltage to the battery. This is like jumping a car with another battery. If you hook it up long enough then the battery voltage will go up, the jump battery voltage will go down. There will always be some AC ripples on the DC if the charger is plugged into AC unless you have a BIG FAT capacitor there to smooth it out. BIG FAT capacitor is expensive so draws your own conclusion. AC ripple does not hurt the battery so very few manufacturers put a BIG FAT cap in there.
As for AC component superimposed on DC. Actually the new and expensive charger with de-sulphate circuit uses the exact principle. High frequency AC superimposed on the DC to break up the sulphate, if any.
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