Given they are going for low cost mass produced, I doubt they have the necessary hardware, especially the highly accurate clocks.
If you're speaking theoretically, yes, again the hardest would probably be the clocks, but there's no reason a private company can't produce them if needed. The bigger issue would be that they would have to compete against the free, government-subsidiesed networks, which seems really tough. Maybe if they target the really high accuracy only available to the military, but even then codeless is already good enough for most applications.
I had autonomous vehicles in mind, which would certainly benefit from a highly accurate, ubiquitous and reliable positioning system (esp. if companies like Tesla can be supplied directly by SpaceX).