The ProSine does NOT augment incoming AC current, in the same way the Yamaha uses its batteries to augment the generator output.
If the incoming AC voltage drops too low, the transfer switch in the ProSine switches, totally replaces the incoming AC, and CARRIES THE WHOLE LOAD with clean power totally generated from battery power. That can mean 370+ amps from the batteries if the AC requires 37 amps to start.
It can also TOTALLY REPLACE the incoming AC if it gets out of frequency tolerances, which won't be the case with a Honda generator.
The Pro-Sine does NOT "condition" incoming AC power, but can TOTALLY REPLACE it with clean AC generated from the batteries, if it is "dirty" with quick rise time voltages.
How they operate is explained in my post here
Intermittent high current draws from the batteries, such as those from AC startup, are usually replaced by charging, but continuously dirty or low voltage power can cause the ProSine to drain the batteries fairly quickly.
Just to be clear about it.