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A wild card technically does not “become” core. A new card that is an identical copy of the wild card is added to core, and might later be removed from core again. The wild card never ceases to exist, but is pretty hard to find in your collection while the core card exists. (The collection manager always prefers showing the core card over the wild card; you only see the wild card when you select that specific expansion).
Since the wild card is a different card, disenchanting it does just that, disenchant it. Card gone, more dust. You won’t get it back, why would you? Note that the wild card is not “automatically” disenchanted, if you did so, you did it manually.
Not that I am aware of.