Contact your local building department and ask them this question. Every city and county make their own rules. You might also check with a local contractor who does room additions in your area. They may be able to advise you of your chances of getting the addition permited after the fact. You should offer to pay them a consulting fee, as they may get no further work from you.
In my experience, usually, if a room addition was done by a contractor or knowledgeable homeowner in good workmanlike fashion, conforms with building code, and has been on the property for some time, you can get it approved. You will have to provide plans or some equivalent (again up to your local bldg inspectors), they may need to open up a wall or two to check that proper materials were used, you will have to pay the permit fee and the inspection fees and that will be that. If, however, the addition is clearly not up to standard, it might be less expensive to tear it down and start from scratch.
Hope this helps and Dare to Dream.
Real Estate Consultant
RE/MAX Palos Verdes Realty