I used cf back strap with conventional dual action truss rod on my latest project. I'm pretty sure that back strap made the neck a bit stiffer. At least it needs quite a lot more force to bend it, especially in the way strings bend the neck.
It may have, if your standard neck design is fairly flexible in the 5th to 12th zone. In that case, the backstrap would stiffen it up some.
You can work with that, shortening the length of the backstrap to bring the stiffness down, if you like.
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