Investiture resists Investiture, since the Unmade are relatively 'equal' I'd say no she couldn't. She can only 'enlighten' Radiant Spren with their permission.
For 'un-corrupting' I doubt it, it seems like a permanent transformation. After all, turning someone into a Steel Inquisitor or a Koloss is effectively permanent, and Enlightening could have some correlations to that, sort of.
As for corrupting an entire Shard? No, absolutely not. She is still just a Splinter, Odium could probably kill her with barely any effort, he just doesn't because she's too useful.
I'd say that Divine Intervention would be just as rare as finding the Distilled Essence of a God.
This seems like a similar question to 'Can you fuel Awakening with Stormlight instead of Breath?'. What you want is possible but no one onscreen in the books has figured it out yet.
Also we have no idea what Burning Raysium would do so that's a 'maybe' from me.
JustQuestin2004's post in can Sja anat corrupted other unmade? was marked as the answer