The antipope Jorge Bergoglio is no authority to perform the Consecration.
Agreed. But I doubt he'd ever do it anyway, unless he were to convert (and you're a sedeprivationist and believe that he would resume formal office at that time).
There's one prohecy which speaks of a Black Pope and a White Pope dying on the same night, and after that would be the Triumph of the Church. That could very well be Bergoglio (Jesuit superior often called a Black Pope) and we have Ratzinger walking around Rome in papal white. So I suspect that those two will die the same night (they're both pretty old).
There's another prophecy (I believe from Blessed Anna Maria Taigi, if I recall) that during a conclave Sts. Peter and Paul would appear to designate the next pope to be voted for. That then would be the Holy Pope. And it's that Pope who I believe will consecrate Russia to the Immaculate Heart of Mary, but not until the major chastisement breaks out. Will Bergoglio and Ratzinger live another 7 years? Quite possibly. Despite protestations of poor health from Ratzinger in 2012, it's been 10 years now and he's still fine.