The article quoted by @raum makes a point that I disagree with:
“Note that a functioning sociopath or psychopath (one with sufficient empathy to get along in society) would still show up as human.”
A functioning sociopath or psychopath doesn’t function in society because they have “sufficient empathy”. They function because they are able and willing to fake it. The functioning psychopath can answer the questions themselves in a “human” way but they can’t fake the biological response (like dilation of the eye for example) any more than a replicant can.
So I think that they absolutely would fail the Voight-Kampf test.