Fail in the election as he did，he became famous for his fiery speech against slavery.
Dislike him as we may，we must acknowledge his greatness
Are these two sentences correct? Is it normal or idiomatic to use 'as/though inversions' like that?
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The second sentence is closer to the more common phrasing ("tired as I may be, I will still complete my work"), where it would be the same as saying "even though I'm tired, I will complete my work". The first sentence just sounds a lot more unusual even though the meaning is still clear: "Even though he failed to such a degree in the election, he became famous ..."
To answer your other question about whether this is normal or idiomatic, this kind of sentence may have been used often in the 1800s or early 1900s, but definitely not so much now. Even the second sentence seems rarely used in modern writing, and nobody would write something like the first sentence now, it just seems too old-fashioned.