Ignore Nomy, she forgot someone on here is actually interested in this stuff and is actually being schooled in it :v
But no, it wouldnt - or rather shouldn't. Much like other diseases, Avian Influenza most likely is carefully picked from the flocks and often removed and isolated either until the infected recovers, or more frequently, is euthanized due to the expenses it would take to recover it. In addition to it, there is a high pressure on producers to provide the best kind of meat and often even small thigns such as stress in the slaughter process can greatly harm the marketability of the meat, so something like Avian Influenza would probably be rather unmarketable even if they weren't picked out and isolated and even if the FDA allowed such meat to pass. (Since there are strict observations typically done)
So its considerably unlikely that a chicken that had Avian Influenza ever made it to some packaged chicken noodle soup. Perhaps there is a small chance but a quick google search also says that even if it did, if the chicken was cooked properly, it would not be a problem anyways.