The extent of the damage depends upon two things.

If the wood is broken, the plant is weak and will need to be nursed back to health and mechanically stabilized so it can't move and be damaged more.

If the bark is broken, it is exposed to disease and possible death. The living part of the plant is the cambium layer just underneath the bark. It is the green layer you see when you peel the bark off a woody stem. If the cambium layer is exposed, it will die. The bark protects it. Even if the cambium is intact over most over most of the plant, cracks in the bark can allow disease to enter. If the damaged cambium layer completely surrounds a branch, the branch will die. There is no saving it (except by heroic measures such as bridge grafts). That is what is meant by saying something is girdled. For a branch to live, there must be an unbroken cambium layer from the roots to the tip of the branch. The part beyond where the cambium layer is girdled will die.

Some azalea will regenerate from the roots. So even if the top dies, prune back the dead part and wait several months to see if any sprouts come up from the roots.