halacha - Can the daughter of two people who could not marry a Cohen marry a cohen?

Can a woman whose father's father isn't Jewish, but whose father's mother is a regular Jew, and whose mother is the child of two converts marry a Cohen?

On the one hand she isn't purely from converts, on the other hand the side that purifies her from that would also forbid her to a Cohen?

Would the answer be different if the Father and Mother's situation were reversed?