It's not that virginity has magic effect on them in this world, it's that they, being pretty smart, trust virgins and are willing to let themselves be seen by them, but it doesn't override their sense of self-preservation.

After all, the one in part 1 was running away from Raynd's gun even though she was a virgin and the unicorn was with Rose, also a virgin.

I dunno if Darkwood unicorns would be willing to be girdled even by a virgin, and they strike me as the type to bolt once they knew something was up.