Note: Don't list them if there are, I just want to know if they exist.
I have noticed that there are several posts on meta asking for secret badges. This answer suggests they are being considered, but have they been implemented?
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Since this feature request hasn't been implemented, and presumably they're still "thinking about it", I'd say the answer is no.
Further, I'd expect if there were, someone would have already been trumpeting about achieving it.
Since we've not seen that, I would take that as strong evidence of a lack. (If the badge is a secret and no one can get it, does it really exist?)