Is it possible to use "Animation Nodes" when exporting it to a game engine? I want to export an animation to Godot game engine. Would that game engine specifically support the use of "Animation Nodes"
As Duarte Correctly pointed out, animation nodes are Blender exclusive data. If you use a format that supports animations, such as Collada or Alembic, you should be able to export the animations as keyframe animations. However, this will only work for the basic location-rotation-scale animations, things like mesh deformations created with animation nodes will not be exported. A similar question has been asked here if you want a bit more info: Blender page animation collada file in Scenekit

If you have any issues, you can also check out this question that the creator of the addon answered: Convert Animation Nodes to Object and Keyframes