No fert through the pivot. Corn and cotton are fertilized by knifing liquid nitrogen (and sometimes amendments like zinc), into the beds right along side of the plants — this is done with a rig that attaches to a tractor. Corn is also fertilized at first with a starter solution that is put in the seed furrow by the planter. We also occasionally fly pelleted fert on corn with an airplane. There have been times when we applied foliar feed to the cotton with a spray rig.
Sure seems like a liquid fert and pesticides through the pivot would save on fuel, time and aerial spraying.
One of my short lived jobs as a teenager was flagging for a Crop duster applying something similar to DDT on cotton. I remember my dad applying DDT to his garden...