Can I apply ceramic coating without paint correction?

You can, but the coating will preserve whatever is underneath it, including swirls, haze and water-spot etching. On paint in good condition, a light polish may only be needed to refine gloss; on paint with visible scratches or swirls, correction before coating is what produces a good result. New cars often need polishing too, because transport and dealer preparation commonly leave fine scratches and swirl marks. At minimum, the paint must be thoroughly washed, decontaminated and free of oils before coating.