Clogging of pores in the skin, as well as lack of omega-3 fatty acids, and an increase in oil production may be causes of acne. Vitamin D isn't a contributor.
Many may disagree but I would say no. Vitamin D aids the body in repairing and developing bones and teeth. Acne is caused by a lack of water, usually aided by caffine and soft drinks.
Many people claim that vitamin-D (sun or supplements) have improved their skin. Other things like harsh soaps, stress, dirty pillows/blankets, touching the face, and bad hygiene can cause acne.