Does pcos affect the results of an ovulation home test? And how does an ovulation test work?

Possible. The ovulation predictor kits are testing for the lh surge. With pcos the lh is chronically elevated, possibly giving a false positive test.
Sometimes. An ovulation kit works by measuring a hormone called lh which eventually accumulates in your urine before ovulation. Many women with pcos have chronically high levels of lh which can cause a false positive urine test kit. In others it works just fine.