Hey I'm an appraiser, thought I'd chime in.
1st off, if the appraisal is for a bank loan, the appraiser does not share the results with the local taxing authority.
2nd we are required by most companies to take photos of all outbuildings regardless of their use/shape. Any outbuilding not on a permanent foundation is considered personal property and not assigned any value.
3rd I personally have never given any value to a coop, not to say I would never, just haven't yet.   Barns and workshops are the type of outbuilding that typically would increase value.
4th property values are down all over the place. I hate going and meeting good people, knowing that a refinance would help them out considerably and then turn around and not be able to appraise their property high enough for them to qualify.   I want out of this line - but thats another topic.