Makes no difference. The rationale or basis for the doctrine is to minimize chaos. The doctrine is not always applied. There have been improvidently seated officials whose decisions were ditched, but that typically happens when the decisions affect a small number of people, like "one."
There would be considerable political and public pressure to remove Sotomayor and Kagan from SCOTUS, and perhaps other judges; but their participation in past cases would not cause all of those cases to fall out, and those judges would very unlikely do the honorable thing and resign.
ph
See my fixed reply to jjotto above.
IMHO and totally uneducated and non-legal background opinion, the situation with 0bola/Zero is without any precedent and should be adjudicated in a different manner.