This seems like mainly a Phaser question. Can you write an app without Spine that shows a simple, rectangular texture and allows you to draw on it? If so, then you can probably do the same to draw on the atlas textures that the spine-phaser runtime draws from. The hard part is probably deciding where on the atlas textures to do the drawing.
As you mentioned, you could render the whole skeleton to a texture, then draw on that, but that's drawing on a static image. It's not the same as drawing on the textures that the skeleton is using, as the skeleton could continue to animate. You can't render the whole skeleton and then somehow update the atlas textures from that. You'd lose information where the textures overlap.