Hi,
Many variacs say to not turn the dial with a load on it. I would not be turning the load down to 0 volts before shutting it off. Rather I would shut off the charger first, then with no load you can adjust the voltage.
I had been thinking of using a 10 amp variac to recharge a electric car project I have been thinking about. I would be recharging a 72 volt battery bank, and use the variac to control the input voltage to a home built rectifier.
2 amps at 110 volts is about 220 watts, while the charger input is around 150 watts with output being 10 amps at 13.4 volts. So you should have about 30% more capacity than the charger input. Yet be careful that nobody puts the charger on "Start" mode, even for a little while, that mode will have about 20 amps output at 15 volts or so, more than 300 watts output, so much more than 320 - 330 watts input. Still not enough to trip a 3 amp fuse on the Variac, so be careful.