Provided they don't mess with the form, a valid priest using the NO Confession form would confer valid absolution. You only need "I absolve you from your sins" ... and even (if I recall) the in the name of the Father, and of the Son, and of the Holy Ghost are optional ... though if they adulterated that into "in the name of the Creator, Redeemer, and Sactifier), that might invalid it.
So this Sacrament as do a number of others, rests upon whether the priests has been validly ordained.
Most SVs hold that the new Rite of Episcopal consecration is almost certainly invalid, but at the very least 100% meets the threshhold of positive doubt. Then any priests ordained by bishops consecrated in that New Rite would be doubtful also. If there WERE some priests ordained in the new rite by a bishop consecrated in the old (an incredibly rare scenario these days), many SVs hold that even the rite of ordination to the priesthood is also doubtful (I agree with this).
That's a tendency only, however, since one could in theory be an R&R and hold the same position (as quite a few do), or there's an occasional SV who would hold that the New Rites of Holy Orders are valid. So there are tendencies, but R&R vs. SV are positions that are technically formally distinct from the question of the validity of Holy Orders. Where there might be some overlap is that if you believe in the Disciplinary Infallibility of the Church, a legitimate Pope would be prevented by the Holy Ghost from isssuing an invalid Rite of Ordination. So that's where there might be some interplay. But then many/most R&R rejection the notion of Disciplinary Infallibility and draw their conclusions that way, thinking that he's a legit pope but promulgated doubtful Sacraments. For SVs, that's an impossibility.
Topic: Is there any case where you all think the Sacrament of Confession by NO is Valid (Read 811 times)