Even though the NKT has distanced itself from "mainstream" Tibetan Buddhism it should be viewed as having traditional roots. The meaning of roots, in this instance, is the beginning teachings and practices like Lam-Rim and Lojong. The NKT still has all of these teachings and practices, they have just be misguided. This misleading is probably why many people think it should not be viewed as having traditional roots in Tibetan Buddhism.
I believe the New Kadampa Tradition should be viewed as having traditional roots in Tibetan Buddhism. The reason I say this is because the New Kadampa Tradition does have traditions rooted in Tibetan Buddhism. This is not a matter of debate. The question poses a question about something that is pure fact.
Yes, the New Kadampa Tradition should be viewed as having traditional roots in Tibetan Buddhism, because if it is not an offshoot it is a parody. There are some things that are different, but it fits loosely within the definition of Buddhism. I would liken it to what the universalists are to Christianity.
This is like asking if one of the many dozens of sects of Christianity should be viewed as having traditional roots. Of course it does. It's just an interpretation and a branching off from the norm. It's still based on the scriptures of Buddhism, therefore it has traditional roots as well.
I do not think that the New Kadampa Tradition should be viewed as having traditional roots in Tibetan Buddhism. I think that the religion of New Kadampa Tradition is too radical and eccentric to think that is has any roots in Tibetan Buddhism. I think people should be allowed to follow it though.
The New Kadampa Tradition subheadlines itself as the International Kadampa Buddhist Union. It comes from the Mahayana form of Buddhism, which was developed from the Gelug school of Tibetan Buddhism. So I know that all that stuff is important details to practicing Buddhists. But the bottom line is that yes, it has roots in the Tibetan tradition.