Everything justalayman said is correct. It really will depend on the building standards department in your jurisdiction. However, I think the most likely scenario will be that the addition will be inspected to see if it meets code (most likely current code). If the addition does not meet code, then they will likely give you an opportunity to bring the addition up to code. I've even heard of people receiving code variances in such situation. For example, if you have a 10 feet setback requirement and your addition comes within 8 feet of the property line you may receive a variance even though code says this is a violation and the structure should be removed from within the setback.
Whether the additon meets code or not, you more than likely will still have to pay permitting/inspection fees. Most jurisdiction will not levy excessive fines for residential violations such as yours and even try to work with violators unless you're a repeat violator or your construction has adverse impact on neighbors or the public. An adjustment to your tax assessment is also likely, however, I believe most county/city tax laws will have a limit on the time period corrections to property evaluations can be done.
But again, all this will depend on your jurisdiction, ordinances/policies and the people you'll be dealing with. Good luck!