Operating system: Ubuntu 18.04
Graphics card: GeForce 750 Ti
Grease Pencil animations do not show up in the Action Editor.
I understand that the functionality for the Dope-Sheet and Action Editor aren't meant to accommodate GPencil's frame-by-frame nature, but I believe creating and saving Actions in the Action Editor could prove useful in the long-run.
For example: Creating complex 2D animations that can only be done frame-by-frame, and then simple rigs with the Action Constraints that allow switching between those animations.
Such a system could potentially help Grease Pencil leap beyond mere Cut-Out animation with deformation rigs and into something that's more of a hybrid of cut-out and traditional animation. It can do so by taking a more modular approach to tradition animation. (I'll even happily create a tutorial for all this.)
It seems that @Joshua Leung (aligorith) initially intended for such a feature back in 2008: https://blenderartists.org/t/animation-dev-grease-pencil-mode-what-does-it-do/420905/61
Another interesting use-case for such a feature is, of course, with the combination of the NLA Editor.