It would really depend on the person. If you had an acute disc injury and had bad pain first thing in the morning, you may want to wait a little longer to perform the exercises.
However, if you are just talking about a preventative program or a less acute problem, I don't think it would be as much of an issue. I wouldn't roll out of bed on to the floor and just start knocking out some reps, but if you did some kind of warm-up like walking and some mild stretching or dynamic warm-ups, I think the exercises would be fine.
The exercises you mentioned do not place the back in a flexed or significantly loaded state. Do the cat/camels first in the series of exercises you mentioned. The ab curls I would probably leave until last. Also, you could perform some press-ups prior to and after the curl ups further decrease possible injury.
You are correct in that the most important thing is to avoid significant spinal flexion as well as compression, first thing in the morning.
Let me know if you have any other questions. If you haven't read his book Ultimate Back Fitness and Performance, I would highly recommend it.