The original is no good in AmE, though it may occur in BrE. I would expect this as natural: He has never sung in Seoul , but he has done so in Busan. Here, 'done so' = 'sung'.
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cho7712He has never sung in Seoul, as he has done in Busan.Isn't this what you mean?
cho7712it seems the adverb isTrue. The adverb is not always recoverable.always notnot always recoverable