But what of the average NO parishioner who isn't aware of these possibilities ? Invalid ordination, lack of true intent by a priest, etc.
Would God deny pardon to these sinners who leave the confessional believing they have received the Sacrament ?
I believe that this is the kind of question that we cannot know for certain the answer. In this, only God can judge the true disposition of the penitent. Forgiveness should not be
assumed.
This is this kind of questioning, I think, that caused so many other problems.
The concept of "invincible ignorance", for example, evolving from the certain doctrine that a lack of knowledge of a particular doctrine on the part of a Christian will not damn a soul to a sort of "get out of jail free card" in which the whole of humanity is saved through ignorance of the True God.
Another example is the New Religion's doctrine that aborted babies most certainly go to heaven.
We have to recall that, while God is perfectly merciful He is also perfectly just. Perhaps God will give such a Penitent some level of grace due to his own true disposition with regards to his sins (as He does in the case of a perfect contrition), but the priest cannot give to the penitent what he himself does not have to give--and that is true absolution from sins.