You may be right in that it is unlikely the bird would look so much Sussex after a single cross but it is not outside of the realm of possibility that the bird does have the gene. Given that color of the egg is easy to select for when picking eggs, it would be easy to breed it into a bird that a breeder prefers the looks of unless the gene is tied to specific traits like red hair is to freckles but I haven't read this is the case. It would be best for OP to contact the breeder as he or she would know and would be able to correct any mistakes in selling the wrong breed bird.