I think so. The camera getting dirty problem isn't a real problem, you can just have a glass window with a stainless steel wiper that scrapes it clean.
That said I'm not that upset if they don't allow them. Nicer cars often have fairly aerodynamic mirrors (long thin stalks, "bullet nose" housing extending a good amount forward), which you could make some custom clear fairings for if you wanted to lower drag further.
Another option is to buy convex racing mirrors which would get you probably 75% of the drag reduction of cameras. Only downside is they can't be adjusted, but that's perfect if the seat also can't be adjusted
