Yes, a nuclear Iran would spark an international arms race, because Iran harbors many terrorists, and they have made many threats against the United States and other nations in the past. Iran is also situated very close to Europe, and Europe would have to build up their arms in order to respond to a threat from Iran. All Western nations would have to build up their arms to respond to Iran.
Nuclear weapons sparked an arms race when first used in World War 2, however nuclear weapons have become too commonplace and prevalent in the world to spark an international arms race, regardless of whether or not Iran is included in the nations that have nuclear weapons and admit it. Many people are already of the opinion that Iran has nuclear weapons, so if they publicly admitted to having them, not much would likely change.