If intention is the raw material, is faith the glue that holds it all together and transforms it into something useful?

Yours is a prosaic description and understanding, that the two go together, as faith is necessary for intention to be acted on by the divine realm always. Although we prefer the term "belief" as "faith is the enaction of a degree of belief more so than a state of completion," and so it implies a clinging, a holding out of hope more so than having supreme confidence in knowing what you wish to happen will be so. So again, level of belief in the divine and in the self as well are crucial in having an intention acted upon by the divine realm.