No, I think the idea is that the Gospel of John is a catholicizing co-optation of Gnosticism. It's just like the religion's debased use of pagan symbols for Christmas.

What John evidently rejects is the substance of Gnosticism, which is the understanding that there's such a thing as religious knowledge ("gnosis") for average Christians. It's not that Gnostics are doubters, but that they take themselves to have independent sources of knowledge of theological matters. By contrast, according to the Church that would become orthodox, Christian faith (for the masses) should be blind. The masses should trust their church leaders rather than claim to have reasoned things out for themselves based on experience.