It gets somewhat close with 3 batteries.
According to manual, connection to iOS lasts over 4 hours. Above 1 hr with Android. I wouldn't think it should not be that drastic since max USB power is 500mA, which leaves 2100mAH left for the remote for the first hour.
If iOS lasts over 4 hours, then remote uses 650mA. Remote should last at least 2 hours with Android with those numbers.
I plugged phone into the Remote Control and opened up Ampere and let it sit for 5 or so minutes, max current draw in that time was 310mA.