For many others, this may be some diastraction such as headphones. There is always a small portion of the Down syndrome population who is extremely phobic and will not cooperate ever, no matter what is done to establish trust. This group also includes very strong gaggers who cannot cooperate. A few people with Down syndrome fall into the severe or profound range of mental retardation and will never understand. In the US now this is very safe and the anesthesia is usually kept at low levels for general dentistry.
Oral surgeons can safely do general anesthesia in their offices.
Anesthesiologists are better than nurse anesthetists. All anesthesia personnel are aware that special needs people present more risks than non-disabled people and they take this into consideration when they recommend anesthesia. If you are skeptical about this, discuss risks with them far in advance of the procedure. Call the hospital and make a special trip just to have your child prescreened by the anesthesiologist, if you are worried. Down syndrome by itself is not a contraindication to intravenous sedation but some patients have heart or other problems that may be a factor.