Can a stepparent be ordered to pay child support and also seek parenting time for the same child?

Yes, these can both apply to the same stepparent, though they arise from different legal questions. A stepparent who stood in the place of a parent to a child can be found responsible for child support under the Family Law Act or the Divorce Act, since support obligations can extend beyond biological or adoptive parents to someone who treated the child as their own, separately from any parenting time question. A stepparent facing this kind of support obligation isn't automatically entitled to parenting time as a result, but nothing prevents them from also applying for parenting time or contact as a non-parent, based on their relationship with the child.

In practice, a stepparent who has been ordered to pay support because they stood in the place of a parent often has a reasonably strong argument for standing to seek parenting time too, since the same evidence - a genuine, ongoing parental role - tends to support both. The two issues are still decided separately: a support obligation doesn't guarantee a parenting time order, and a parenting time application still has to satisfy the best-interests test on its own. A family lawyer can advise on how these two claims interact in your specific situation.