This isn't really a straight forward question. I think StructuralEIT's initial post is on the right path.
If the column is bent initially, and you install the brace while the column is in an unloaded condition, when you load the column, it is going to try to deflect further. The brace is going to resist this deflection by going into either tension or compression. It will help the column by all means, but, the column now has a horizontal force being applied at this brace location, which is either taken out through the lateral and vertical bracing system, or as shear in the column, shared with the other column the brace is attached to. So, if there is no vertical bracing present, while it is not inducing moment at that location, it is inducing shear which will result in moment. Either way, this horizontal force has to get down to the foundation, whether through vertical bracing or shear.
The point is, you have to look at your entire load path. As such, the way I read msquared48's post, it could be misinterpretted. In a pole type structure, adding a knee-brace UP (like a T-pole supporting a utility bridge), will not reduce your kl/r. Adding one down to the foundation, does reduce your kl/r.