What impact do tooth whitening products have on a porcelin veneer?

Not much . Whitening products do not actually affect the porcelain on a veneer. The color of the veneer will not change when bleached.
No impact. Tooth whitening products/procedures only work on tooth enamel. They will not change the color of tooth restorations ie porcelain and composite resins.
None, per se. The porcelain veneer will not change color. However, depending upon the underlying tooth shade, the color of bonding used to bond the veneer, the thickness of the veneer, and the amount of opaque used in the veneer -- the tooth underneeth may change color and the veneer may reflect this. If you do not want to take a change, then be sure no solution gets on that tooth.
None. Tooth whitening products can only whiten tooth enamel and will have no whitening effect on veneers, crowns or tooth colored composite fillings. Over the counter kits and products bought online may not be safe and will probably not be as effective as having that procedure performed by a dentist. Consult with your own dentist who can properly advise you regarding your specific situation.
None. Whitening products will not whiten porcelain on craowns or veneers...It is possible that it can breakdown the bonding material used to hold the veneers in place...Check with your dentist.