I don't know much about cyclocross bikes, I think they have different geometry, probably tighter wheelbase, steeper angles than a typical hybrid. Lighter than the average hybrid too, they are meant to be race machines. Once you put a rack on a CX it becomes slightly hybridized in my opinion and the lines get blurred.
A hybrid drop bar conversion resembles a touring bike much more than it resembles a cross bike. Cannondale sold the same frame I have with drop bars and called it a touring bike.
The only picture I have of my drop bar conversion, a 1985 Ross Mt. Hood.
Yes it was a race bike, but also a city bike, etc. It even had fenders and generator lights on it at one point, and there probably was a rack on it when this picture was taken.
To get my hands in the same position as they were on the flat bars, I used a tall, short reach stem. Mountain bikes and hybrids have longer top tubes than road bikes and this should be considered if you don't want to change your position.
So glad to see another thread on this subject. It's heartwarming to see hybrids relieved of their hybridness. Salvation!