Not… really.
Hawkins is arguably the greatest of the mystics who sought to unify the Western and Eastern spiritual perspectives. from the standpoint of Western rationalism. He never talked about Christian theology in any of his books save to provide a few scant consciousness calibrations as part of his research.
From reading many of his books, I’d have to say that I would have been surprised if Dr. Hawkins ever even opened up a Bible, let alone tried to personally grapple with it. That’s not to say that Dr. Hawkins’ ideas and teachings aren’t valuable, just that every mystic has to make hard decisions about where and how to position their ideas and the finer points of Christian theology simply didn’t seem to interest him.
The calibrations he does offer paint a picture of Judaism slowly raising their level of consciousness to a sudden ascension with Jesus reaching the peak of a full 1000 level of consciousness, the highest possible among humans. Slowly as Jesus fades from direct awareness, the level of consciousness of his followers steadily drops reaching a low point right around the Protestant Reformation, which kickstarted what we would consider the modern world, with consciousness steadily rising ever since.
Hawkins stated that only five humans ever reached 1000 in life. Jesus, the Buddha, Zoroaster, and, strangly, Lord Krishna and Ahura Mazda, both of which are deities, but perhaps he was considering their incarnations, Krishna is said to have incarnated. I never understood the inclusion of Ahura Mazda in this calibration.
Another connection to Christianity is that Dr. Hawkins placed great value on both A Course In Miracles, stating that it can bring you to level 600 if you follow the course faithfully, and Alcoholics Anonymous and 12 step programs in general, stating they can get you up to around level 500 if followed faithfully. Both are very heavily “surrender to a higher power” teachings and Hawkins placed great value on surrender.
There are the very few Western connections, because his theology was predominantly Eastern. He even used the term nonduality to frame his perspective on enlightenment. He does state that “Christ Consciousness” is the same thing as enlightenment, as everything relates back to the scale and anything over 6–700 is enlightenment. He never defines Christ Consciousness as far as I’ve read.