I feel if you want to think of those weeds as your "Cover Crop" that is perfectly okay.
I think of a "cover crop" as anything that helps keep the wind from causing erosion and puts nutrients back into the soil. Those weeds probably fit that description since you are doing "chop and drop". Free nutrients.
In agriculture, cover crops are plants that are planted to cover the soil rather than for the purpose of being harvested. Cover crops manage soil erosion, soil fertility, soil quality, water, weeds, pests, diseases, biodiversity and wildlife
Cover Crop
It will be fun to see what others feel.