I would doubt that the surface of melamine board is anything you'd want to paint - it's not a 'flat' surface. It's similar to what's behind Formica(R), as it's just a 'faux' hard covering over a similar melamine type board. The underlying board is the real savings for the manufacturers, so it's not going to be any good surface to do anything other than 'cover up', just like the original.
I used to have a customer in my town who did this very board 'covering', which is similar to a 'hard' wallpaper, and supplied them to the industries that make use of them, such as furniture makers who sell the 'build yourself' or 'ready to assemble' type of office desks, cabinets, etc. It's just easy to cut 4 x 8 sheets that manufacturers can easily customize to make their own RV cabinetry, since all of their cabinets are made at the RV factory, and not purchased and shipped in as finished items.