Your power calculation is correct. A 120 volt RMS sine wave actually goes from -170 to +170 volts, but use RMS for power calculations.
When charging a battery, you have the right idea, but you should be aware that charging a battery is not 100% efficient. That is, if you put 10 kW-hr into a charger/battery combination, the battery will not be able to put out 10 kW-hr. Charge efficiency is quite high during the early stages of charging, but gets less efficient toward the end, when the battery is nearly charged (the term for this is State of Charge, or SOC, which runs from 0% - fully discharged, to 100% - fully charged. Charge efficiency reduces as SOC increases). As a very rough number, for large lead-acid cells assume overall charge efficiency is about 50%, so your example would require 116.66 hours. Since the 50% number was not precise, call it 100 to 110 hours.