Seeing this question here and that you PM'ed me this question almost verbatim, I decided to write my answer here for the public's benefit.

The short answer is no.

The long answer is that the public key can not be used to guess any bytes of the private key (including the one at the end which we tend to call "parity") using only cryptographic primitives. You need to get this information from side-channels, i.e. CPU frequency analysis when a point is being multiplied by that private key - and it requires physical access to the hardware that's performing the EC multiplication, usually the one that's running the wallet.