Were proper permits obtained when the addition was constructed? Was it inspected and given a certificate of occupancy as living space? If it was inspected and passed did the assessor assess it as living space? Unless you checked how can you be sure that the house was reassessed to include it as living space after the addition?
If they did, how is it that the Realtor is qualified to tell you that it is not 'living space'? Can the Realtor cite some code or law that would be controlling on this point?
Does the addition have the same quality of materials as the rest of the home? It sounds like it might be a covered patio that was closed in. Typically I have seen appraisers only give these kind of additions about half the price per square foot as the main home. If it's a true addition to a home with similiar materials or better than the main home plus it has it's own heating / cooling system you would be able to get a higher value for the additional square footage of living area. If you would like a true non-biased opinion from a 3rd party, hire an appraiser for about $350 and you will get an accurate square footage measurement and a professional opinion of your home's true value. Appraisals are great to use as a tool to help you get the most for your home. If you need a referral, please send me an e-mail and I will give you a guy's name who is great to work with.
You have anther question to answer before you put in that window unit.
Some residential areas have restrictions against window units, have you checked this out.
In our area homes in the country that are part central air and part window unit, such as an addition you have, are being put in the MLS as the total square footage, are being taxed as the total square footage and being appraised as the total square footage, but things may be different in Dallas.
Now if you have a detached room or garage that you have converted or you have converted the garage, you do not have the same quality and density of slab and you want to call that part f the home. The answer it no. It does not qualify &/or meet the building standards of the house.
Either way I believe the small investment in the window unit, if allowed in your neighborhood, would be a great investment for you. It would lower your electric bill while you were still in the house and make the house more attractive to potential buyers.
Your selling agent could at least advertise ____?__ft livable area - explaining the add on.