Can people with both genitalia get pregnant?

Yes: If there is a open vagina that leads to a viable cervix and uterus, as well as fallopian tubes and ovaries connected to that pathway, absolutely yes. Often in these cases when they are identified as infants, one set of genitalia are removed at the urging of the md and consent of the parents.

Basically no : You are referring to the concept of being a hermaphrodite. There are a wide variety of manifestations of this condition and varying degree of phenotypic expression. As a general rule with rare exceptions hermaphrodites are infertile.