To the best of my knowledge, if you are paying cash for any property you are not required to get an appraisal. That being said, I have seen homes where the purchaser paid cash, did not get an appraisal and then needed to sell the property only to find out they paid too much. Because of this, I always recommend getting an appraisal to my clients.
Please note that on this property, they want the buyer to pay for a City Inspection once the offer is accepted. The City was very good at finding problems with my home, especially those requiring permits.