I would say that the answer is "yes" based on the example of Sheba that has been given to us. However, I wold also point out that a woman or even a normal man do not appear to be the first/best choice as in the example of the Isralites when they asked for a King...God made "Saul" king over them, when they asked "why?" they were told: "because God favored him in his size and knowledge".
Interstingly, this teaches us that the best person for the job is not always the obvious one.
- The Isralites had a prophet in their midst, yet God chose Saul for his qualities - physical stature projects power.
- Moses was the one chosen as prophet, yet God allowed Aron to be the spokesperson for the message because he was more elequent.