No. No more than the Prom Queen can be said to have the power to legislate for your high school, or that coronation of the Erie County Strawberry Queen shows that Erie County is a monarchy.
You have to discern what kind of queen you're talking about.
In the case of Mary, it's strictly a relational thing: Christ her Son is King of Kings; that makes her Queen Mother by relationship alone. It does not indicate personal sovereignty.
It corresponds to an outstanding Biblical image:
"A great sign appeared in heaven: a woman clothed with the sun, with the moon under her feet and a crown of twelve stars on her head."
And what does it make Joe?
And that woman is Israel....
Then why pray to her to ask her for salvation and grace, and help and healing??? And to answer prayers if she has no sovereignty???