Usually, yes. However, there are cases in which the priest does not possess the requisite faculty by office or by delegation, but the faculty is supplied by the law itself to cover the situation. This would concern emergency situations where a faculty could not be granted quickly, emergency situations where a laicized priest could give absolution, or when there was error on the part of the penitent as to whether the priest had faculties. This supplied jurisdiction only applies to the faculty to hear confessions itself, and not to anything lacking in the essential nature of the sacrament, I.e. the formula being said correctly.
-ACEGC