I am having a similar issue with Layer Comps. It isn't that Appearance isn't holding true it is the position of the elements. I move elements to a certain position, update the layer comp, switch to another layer comp then back again and they moved all over the place.
Sad to see there has been no response to this post.
I'm having the exact same issue with layer comps not performing correctly in regards to Color Overlay, when the document is saved and then re-opened.
This bug has been around since ages, and still present in Photoshop CC 2015.1.1 (latest update).
Please fix this annoying bug, as it is almost impossible to work with layer comps using color overlays.
just updated to most recent version today and bug is still there (unless it's an undocumented feature).
Only workaround I've found is to have two layer styles defined. One that you want it to change to, and then another to change it back to the original color. and yeah, this bug has been around for ages.