Quite impossible. The Great Rings were made around the year 1500 of the Second Age. Arnor was founded around 3320 of the same Age.
It is quite possible that one or more of the Nine were Dunedain in ancestry, from those who returned to Middle Earth during the Second Age. Remember that Sauron deceived those who took the Rings. There was not necessarily anything evil about the Nine Rings at the time their Ringbearers took them up. Sauron made the One Ring after the others and thereby corrupted them.
The Elves escaped because they refused to wear or use their Rings while Sauron held the One. The Dwarves were not totally corrupted because they were unusually resistant to being dominated. Men were not as discerning as the Elves and were more susceptible than the Dwarves. The nine kings were not necessarily originally evil, which just adds to the pathos and horror of their present condition.
I went back and reread some stuff, and it turns out there's only one Nazgûl to whose origin is alluded, and that's in The Hunt for the Ring in Unfinished Tales. Khamûl, the second in command, is known as the "Black Easterling." This might only be a reference to his habitation as a Nazgûl, but I prefer the other interpretation, because it gives our first glimpse of who the nine originally were.