I don't know if there is an easier way than this but here is what I do:
1. Use Adobe Capture to convert my photo into a vector, which opens seamlessly in Adobe Illustrator
2. Simplify and organize layers & groups in Illustrator
3. Bring that into Character Animator
You can, but it works better if you do a bit of massaging afterwards in order for eyes and mouths to work. I took photos of a stuffed toy. I then photoshopped out the mouth and eyes.
I then added them back as layers in the Photoshop file. (I split the head from the body as well, but I did not really need to do that.) (Actually, this was not the final file - I cannot find it just now - but hopefully +Left Eye gives enough of a clue.)
So when turned on it looks sensible again.
But Ch can move the eyes and mouth etc. I only did one eye above, the "Left" eye (on the right above). Character animator does all the clipping etc to make it look correct.
My son then did a quick video Wookies! - YouTube