A private key of -d is equivalent to a private key of n-d, where n is the secp256k1 curve order. In other words, there is nothing special about such a private key, as it literally just wraps around.
Further more, there is no way to get any information about what number range the private key lies in, just based on the public key. If there was, it could be used to break the security of the elliptic curve and compute the full private key for a given public key.
So, no.
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