Yes, particularly carriers like American Airlines who have very little paint in their livery, most of the aircraft is just unpainted aluminium.
Wax is not used, but they perform regular polishing, or "buffing", of the exterior unpainted panels to maintain the bright finish, and in fact calculate it costs them more to do this than to maintain paintwork in good condition. There is an assessment that dirty exterior aircraft add to drag and thus fuel costs.
The "car wash" is done from time to time on all aircraft, often in front of the maintenance hangar. Demineralised water is used, another substantial expense in the process. One of the worst items for accumulating dirt is the sticky residue from de-icing operations, so carriers like Finnair with a lot of heavy winter operation have extra cleaning work to handle this.
Air France is renowned for a white livery, infrequent washing, and filthy exterior aircraft. Possibly aircraft washers are expensive and fuel is cheap in Paris ?
