Sickness from exposure to plug in air freshener?

Is it likely that a cat could become sick from exposure to a plug in air freshener?  Could it lead to swollen lymph nodes?

Yes, cats can definitely get sick from plug-in air fresheners as well as regular sprays. It is strongly advised not to use any of these if you have a pet. Chemicals released into the air find their way into animal's airway causing irritation and allergic reaction which in turn can result in swollen lymph nodes.