Animation poses of Location, Rotation and Scale are relative to the Parent. If there is no parent the operations are relative to the scene.
This means when you parent the animated child to an object it will remain where it is. Playing a pose the object will update according the that pose relative to the new parent.
In Blender you can switch to another frame to show the effect e.g. left or right as this updates the object according to the new frame.
Within the BGE you see the effect as soon as you play an action.
As you do not want that, you should ensure to create the keyframes i while the animated object is already parented.