The American Heritage Dictionary notes about adverbs like hardly that
they are not truly negative in meaning. The sentence Mary hardly laughed means that Mary did laugh a little, not that she kept from laughing altogether, and therefore does not express a negative proposition.
However, they are similar to negative adverbs in that they combine with any and at all, as in “I hardly saw him at all.”
With this in mind, which sentence below would be correct?
A) Putin is hardly popular among Germans, but so is the prospect of a scrap with Russia on Ukraine’s behalf.
B) Putin is hardly popular among Germans, but neither is the prospect of a scrap with Russia on Ukraine’s behalf.
[Source for (A): ‘Was Ukraine Betrayed at Geneva?’ by Rajan Menon, http://nationalinterest.org/commentary/was-ukraine-betrayed-geneva-10306?page=1]
I would say (B), since the idea could be paraphrased as follows: Putin is not popular, but neither is war with Russia. But would this be true for any compound sentence where the first clause contains hardly? Or would it depend on whether hardly is indicating a truly negative quality or a minimally positive one?