Unfortunately, we cannot test for Pacheco's reliably, and often we use sentinel birds such as cockatiels from our own collections, to monitor for this disease. Also, chlamydia may be missed because even though the bird is infected, it may not be shedding the organism Chlamydia psittaci , which causes psittacosis. The test for this disease that most vets use detects the organisms only when shed in fairly high concentrations. But, it may be a worthwhile test because the birds may shed during the stressful quarantine period. Have your vet examine the birds to detect subtle physical abnormalities that may have evaded you, such as old bone fractures which haven't quite healed.
Some people also recommend blood profiles.
I think that this is an economic decision on the part of the aviculturist and does give an added degree of insurance but may not be completely necessary. It can be detected if the bird is symptomatic and proper diagnostic procedures including X-rays are done. Also, papillomatosis may be detected but is difficult to evaluate in the early stages of the disease. Again there is no test for a carrier state, because we again do no know what causes it, although presumably it is a virus. Some other avian diseases are undetectable but hopefully the quarantine time will allow their expression.