I re-read your OP. I think the main issue is whether the person going to confession considers the Conciliar Church (and those who it gives "jurisdiction" to) is actually the Catholic Church. I think if one does, then one would need to go to the SSPX priest.
Yes, absolutely. I see no way around this. I personally believe that the Church (i.e. Our Lord) is supplying jurisdiction to all Traditional Catholics priests in this horrific Crisis, and that normal Canon Law is not in effect, except where it's a reflection of Divine Law of course, when the good of souls is at stake. But from the perspective of an individual's conscience, if a person believes that the Conciliar Church is the Catholic Church and the Conciliar hierarchy is the hierarchy, if you have access to a priest who has jurisdiction (i.e. an SSPX priest), you couldn't in good conscience go to a priest who lacks Bergoglian jurisdiction.
There's a distinction here between the objective and the subjective. I personally believe that it's objectively true that the Church supplies to all these priests, but subjectively the person can't in good consciences go to the non-jurisdictional priest.
So, for instance, let's say, for the aske of argument that the NOM is valid. But I have doubts about its validity. Even though I'm wrong, because of my doubts I cannot receive Holy Communion consecrated at a NOM (except in danger of death when there's no alternative). I've written aobout this scenario before. I see a $100 bill on a table. It's actually mine, but I had forgotten that it's mine and think it belongs to someone else. If I take it, I commit the sin of theft, even though objectively speaking it's not theft.