Brent, I'v ridden the section between Crown King and Prescott on my cyclocross bike several times. That's actually my preferred bike for that ride even though it can be a tad bumpy. It's the longer descents that are the most bumpity and hard on your body on a 'cross bike. I think the section from Lake Pleasant to Crown King would be nasty on a cyclocross bike.
The one issue may be snow/ice in the upper reaches of the Bradshaw Mts. My guess is, given we still have a few patches of ice around 6,000 feet near town, the higher sections by Mt. Union would likely be snow covered or icy. There's also a small section near Palace station that's really tucked away and it too can be icy or snow choked for a mile or more. The ride from Crown King to Prescott is not really hard on its own, but throw in a couple miles of ice and mud and it could get labor intensive quickly. If there's chance of wet road, cross tires are slooow and hard to roll, even when it's not "muddy." On a mtb, no problem.
I think even in the very best of conditions, a one-day ride on that route from Scottsdale wouldn't be an epic day. It would probably be a 15-18 hour ride. Ouch.