240 volts circuit amp
No, your initial estimate is right, you don’t multiply it by 2.

A 2-hot leg connection has equal current in each leg to and from the load (it’s a complete circuit). You can measure consumption  by sensing current over time (amp-hours) on one leg and multiplying by 240V to get an estimate of watt-hours.

Also, since it’s a resistance load you will be measuring real power (power factor is unity); you don’t have to consider reactance.