NEW YORK: Allergan AGN, the drug giant that is famed for Botox but also makes antibiotics and an Alzheimer’s treatment, will spend $560 million to purchase Naurex, an Evanston, Ill.-based developer of antidepressants that can work in hours, compared to weeks for existing depression pills. The drug giant says it sees opportunity in a depression drug that works in a new way, and hopes Naurex’s experimental medicines might someday be shown to prevent suicidal people from killing themselves…