If I got spider veins while on ocp's, will they fade after I stop?

No. Although your spider veins may have appeared while you were taking ocp's. It does not mean that this was the cause of their development. And while hormonal influences do play a role in vein issues, stopping the pill will not make the veins disappear. General rule is once they are there, they are there, and must be treated to resolve, which is easily done by a combination of laser and injection.
No. Oral contraceptive pills is not a risk factor for development of spider veins, which can be seen with or without underlying venous incompetence. Pregnancy, heredity, standing for long hours, aging, and trauma are risk factors for development of spider veins.