Under normal circumstances, x-rays should be taken before an adjustment but after the examination. The subluxation is found on the patient and not on the x-ray, so if no subluxation is found on the patient during the examination than there is little need to x-ray.
I don’t know of any “quick quack schools” that produce doctors of chiropractic, and the actual chiropractic education is actually quite impressive when compared with that of a M.D. or D.O.