Hi,
I had a quick try at this. I created a sphere object and a painted shader. I painted on the sphere with the painted shader, and then connected the painted shader to the colour function input of the sphere default shader. What I painted then showed up on the sphere. When I checked it from different angles it looked how I expected. This was just a quick test, I have no idea what the limitations might be or the best way to do this, but in the simplest case of painting on an object it seems to work ok.
The Painted shader can be pretty much used like any other shader, and connected to lots of different sorts of inputs. It's a bit like an image shader which you paint.
Regards,
Jo