Being that the material Yielded (PERMANENT deformation I.E. "Bent"); the assembly is now weaker as a whole. Just FYI. you can add all the bracing you want, but the material where it bent is already compromised and there is no bringing it back. It is simple Material Mechanics.
While this is true, I'm going to have to disagree with you.
The tube itself in most cases is not bent, it has shifted inside the differential, in result is technically still "straight".
If the tube bends anywhere outside of the differential, then yes you are correct it has lost a significant amount of strength.
Because of the design, most axles that are "bent" have actually had this shift happen, and can be repaired without weakening the design.
If you look at a factory axle, opposed to say a Prorock, you'll see that where the tubes press into the housing has a more significant gap (can't really describe this) than a Prorock.
That is partially why they bend at the housing easily. The only issue you will have bending them back is breaking the plug welds, which likely already happened when it shifted.
Do you see how there is a small gap between the actual tube and the housing it is pressed into?
That is enough to cause an axle seal to leak when the tube has shifted.
Versus this, where there is no gap and the tube is not able to shift without bending in the middle.