You can do it in the editor. The physics constraint sees the changes in the world transform since last time it was applied and it causes the bones to "lag" behind, then catch up using forces. When you move your camera bone, it affects the physics constrained bone. When all the constraints are applied, the camera bone movement affects physics -- not what you want.
The trick is to use a transform constraint where the camera bone X and Y translation is constrained and the target bone is what actually moves the camera. Next, place the transform constraint in the constraint order so it happens after the physics constraint (ie place it lower).
This way the world transforms are computed, but the camera bone hasn't moved yet, then the constraints are applied. The physics constraint is applied first, so it sees the world transforms at that time, before the camera bone moves. Later in the constraint order the camera is moved by the transform constraint, but the physics constraint never sees that movement.
