Can I apply the rust converter on an already painted surface?

Yes, you can do this. However, if the underlying rust is not removed and the edges of the paint are not feathery, then it will not last as long. The product can only treat what it comes in contact with and if a layer of rust is on all sides, it will act as a ring around the paint, preventing any new material from penetrating.

If there is oxidation under the paint, eventually that paint will fail to adhere and it will take the rust converter with it.