No. The Oath deals with Shadow sided elements. It lists the Shadowspawn and darkfriends.
At the end of the day, the Forsaken were Aes Sedai that defected to the Dark One, and became his leaders that speak directly for him, and take their orders directly from him, too.
They were called Forsaken, because they were trusted Aes Sedai that turned against the world, and are darkfriends that lead on the Dark One's behalf, that all made the conscious choice to turn.
Figures that darkfriends 3000 years later idolise as mythological heroes.
One was a world famous theologian and philosopher. Ishamael.
One was a technological research scientist. Lanfear.
One was a world famous clinical psychologist. Graendal.
One was a world famous doctor. Semirhage.
One was a world famous athlete. Sammael.
One was a historian. Balthamel.
One was a musical celebrity. Asmodean.
One was a teacher. Mesaana.
One was a lawyer. Be'lal.
One was a banker. Moghedien.
One was a biological research scientist. Aginor.
One was a politician. Rahvin.
One was a world famous diplomat. Demandred.
All of them Aes Sedai from the Age Of Legends. All of them turned, because they wanted more than the world could give them.
The Shadowspawn are not naturally evolved life forms. They were all built, except for the Fades. They are born of Trollocs. They were made by Aginor after his turn, using human beings and animals in genetic experiments. These are not good people.
They are the sort of people even Joker would hate.