First of all most B&P depts, at least in San Diego, don't keep most records more than about 10 years or so. As a general contractor I'm always dealing with this type of research and it becomes very frustrating at best when you can't always find this information out.
However, should you be able to access these records it would clearly indicate whether or not a permit was ever pulled for the room in question. If there is no signs of a permit but one is required to legitimize the addition for the square footage of the appraisal you should see it the current owner would be willing to do that. It would be in both of your best interest to do so.
He would gain from added square footage which would add to the value of the appraisal and you would gain likewise albeit the current owner would then be able to add value to the sales price. Now if the home is an REO or a short sale all bets are off as it would not be very likely that the bank or the in arrears homeowner would be willing or motivated to put in any time, money or effort.
However, if you really like the home and you think you're getting a good deal then I certainly wouldn't let that stand in your way. I've seen a lot of real buying opportunities evaporate over some pretty petty issues. I've actually been down that road a few times myself. If this home gives you warm fuzzies I say pull the trigger.