Relating input torque on BLDC motor shaft with output current
Assuming the load is able to draw some value of current at the terminal voltage delivered by the generator, then there are two limitations from the generator, whether it's brushed or brushless

1) The engine driving the generator has to supply enough torque. If it doesn't, the generator will slow down, the terminal voltage will fall, until the load is drawing a lower current so throwing a low enough torque demand on the engine. This limitation is instant and you'll notice the engine slow down.

2) The generator has to be able to supply that current without overheating. Improving the generator cooling can help with this. This limitation may take minutes or tens of minutes to become apparent, and if you ignore the smell and then smoke from the generator, it may destroy it.