You're right, rods are slightly stiffer than tubes, but, again IMHO, not enough to make any real difference. A tube is a very stiff structure and, when applied correctly, nearly as strong as a solid rod of the same material.
One of the down sides to carbon/carbon fibre is that it is relatively heavy. The reason people tend to associate carbon/carbon fibre with lightweight products is that it is so stiff that little of it is needed to make a specific part or product. If you can use half the carbon of a rod to make a tube and still end up with nearly the same stiffness, that's the winner in my book.
If Erik's math is correct in that thread you reference, the carbon tubes are still 3x as stiff as the equivelant mass/volume of maple. How much stiffer do you really want your neck? If you were making a skinny neck, 36" bass yeah, maybe you wanna get some square bar to reinforce your neck. For a thick neck, 24.5 scale 21 fret single cut any carbon reinforcement would be overkill (having said that, Wez claims that the carbon bars eliminate 'dead spots' on a guitars neck).
I've got a neck trhough double cut out in the workshop that has three layers of carbon fibre running down the middle of the neck (mahog/cf/maple/cf/maple/cf/mahog) and I can tell you that it's as stiff as a sailor in a stip club. I am avoiding working on it due to the fact that it is killing my tools (as I suspected would happen and even state in the thread that you reference). I'll probably post a pic of it when I get around to finishing it (but I'll be finishing every other project I have first!!).
All the above just my opinion and I'm always happy to be proven wrong, just ask my wife.
Cheers
Buter