I collect bagged leaves in the fall - mine and my neighbors' - and store them in a sheltered area, and then use them in my chicken run year-round. They make a great addition to the run litter! Dry leaves + wood chips + whatever other seasonal yard waste there is (mowed grass, weeds from the garden, Christmas tree branches etc.) is the best run bedding.
I think the recommendation for tree spraying is after the trees go dormant in the fall, so I don't think the leaves would be affected. And even that is only for fruit trees (IF people spray). So maybe check with your neighbors and see if they spray and when. Only one of my neighbors has a fruit tree, and I know they don't spray it.
My main problem with the neighbors' leaves is that they collect them mostly from the front of their properties, along the sidewalk and street, and there's quite a bit of trash in there too

from uncivilized commuters throwing things out their car windows or kids walking home from school dropping candy wrappers. So I have to be careful when dumping the bags in the run and pick out the trash, which sucks. And of course you have to make sure the leaves are dry when collected, to avoid mold, and since I can't check inside the neighbors' bags for dampness, I just keep an eye/ear out for leaf blower noise or raking noise and take a peek (I'm in a thick suburb and can see all my neighbors) so if I see them collecting on a dry day, I only take those bags. Some neighbors know by now and just leave the bags by my house. Likewise they give me their mowed grass, too.
I don't see why taking bags that have been left on the curb would be a problem. It's not like diving through household trash for sensitive information/belongings... It's just yard waste.