No. For one thing she is only the head of the Anglican/Episcopal* church, not of protestants generally. For another, she is really not much more than a nominal head. It is the bishops and synod who make the decisions.
* Correction: It appears, as others have said, that she is head (or rather Supreme Governor) of the Church of England, rather than the Anglican Church as a whole, and so is not governor even of the Scottish, Irish and Welsh branches of the Anglican Communion.