Woud early pregnancy cause an ovulation predictor test to give a false positive?

No: If you're pregnant, there's no ovulation, so i don't see how ovulation test would be indicating that you are near ovulation.

Yes: One subunit of pregnancy hormone HCG is structurally identical to the hormone that is measured in the ovulation prediction kits (luteinizing hormone) and most home tests don't differentiate between the 2 hormones, so yes, pregnancy can give a false + for ovulation.