No in that a step father does not have his own rights to the stepchild; regardless of how emotionally important or valid the child-stepfather bond, a step father is not legally the parent, the way a biological or adoptive parent is.
Yes, in that courts will take a child's best interests into account when crafting custody and visitation orders, and have often, for example, mandated that grand parents or other non-parental relatives be allowed to visit or have contact with a child. Therefore, while a step parent would very likely not gain custody, absent perhaps very exceptional circumstances (parent ruled unfit; no other blood or legal relatives who could care for the child; step parent made legal guardian), it's possibly you could at least be given some visitation rights if it's in the child's interest. You should discuss this with a family law attorney.
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