We cannot say definitively if Aster Yellows is a factor here. There are other issues that can cause these kinds of symptoms (and multiple issues could be overlapping). Coneflower Rosette Mites can cause a strange growth pattern in the heads/cones (and appears likely in this case), sunflower moths could be boring into the cone interior, and various chewing insects (beetles, grasshoppers, earwigs, katydids, caterpillars, etc.) can be responsible for removing petals. If you go out at night and look at the flowers with a flashlight, sometimes the specific culprits can be found/identified. 

The symptoms of Aster Yellows would be different (green flowers, leafy growths coming out of the cones).

Christa