Yes, it is possible, it is however hard to get a good result.
I used this: Elias Wick | Outline to test it. Simply you take the white and black mask of the background and outline. Then get a duplicate and increase the size, finally add a noise texture or noise node to disrupt the first mask, then add them together.
I managed to get this after 3 minutes, which isn’t really what you want:
Depending on how the Outline is generated, you would have to use various methods. In my case, the outline expands from the center, so I would have to offset the outline in order to get the proper look. This means that I would have to rework most of the shader.