Loosely speaking our prayers go up as offerings of confession, faith, thanksgiving, and praise, those being the primary interactions expected by God.
I believe an intercessory prayer to be a prayer of faith, having no intercessory power in it's own right, as we submit everything to the will of the Father, by the authority of the Son who is the intercessor (High Priest). Had we intercessory power of our own, those prerequisites would not apply.
The power of intercessory prayer, be it a matter of soul-saving, healing, imparting of knowledge or discernment and etc, comes from the faith and confidence with which it is offered, ergo it is the earnestness and faith which moves the Father to do intercessory works within His will.
In that sense, 'intercessory' is merely a label to provide for definition, not the act of intercession itself.
Now take what you just said and apply it to Mary and the saints in Heaven. Our beliefs about their having "no intercessory power" of their own absent the will of the Father is exactly identical.
So you do understand the role of Mary or a saint.