It would not necessarily be conclusive. For one thing, if they're HPD and pathological liars then they've probably convinced themselves and the lie is not really separate from reality to them––they simply change the reality in their mind and somehow manage to believe what they want it to be. If they have no conscience or remorse and are cool under pressure, confident that you have no other evidence, it may not trigger an abnormal physiological response. Regardless, a polygraph is an interpretive process and there are people who can reliably defeat it.
My HPD was a raving pathological liar and it still blows me away after realizing the false reality she got me to buy into. On one level of course she knows she' lying but to her it's completely excusable and justifiable due to no fault of her own. She still claims innocence while admitting only as much a I convince her I have absolute proof of even though all the rest is an integrally related part of the larger illusion.
One of the things that showed me what I was really dealing with was when I found something inconsistent I would not immediately let her know that I was suspicious and and then ask questions that required her to tell layer upon layer of lies to cover. Then when I'd finally call her on it I would only present part of what I knew. She would admit to and justify only that aspect and swear the rest was the truth. Then I'd reveal more of what I knew. This really brought the pathology of HPD to the surface and wrapped her in knots.
Here is a web site that had a lot of information on lie detection as well as characteristics of liars themselves and patterns, etc.
http://deception.crimepsychblog.com/