As with much of non-traditional medicine. Most of the results of cupping are simply your body releasing natural chemicals to fight the attack on the blood vessels and skin cells. Most of the people I know that cup are people in the BDSM world that do it for the high that comes from enduring focused pain to that degree.
So, yes it will help you relax but so would an endorphin button or masturbation.
The difference between cupping and hickey are the degree of damage being inflicted which is much greater with cupping due to higher level of suction over a larger area.