I must admit I've never considered this point, and I'm pretty certain at some time I have had both the EHU and the car connected at the same time, and I've never had a problem, but I'm not suggesting its the best thing to do.
But knowing the way the wiring should be installed, and provided the wiring has been installed and maintained correctly, then there should be no danger of anything untoward occuring.
Even if there is a fault, the caravans 230Vac mains input protection system should be able to keep you safe.
As I no longer have a caravan, its not an issue for me going forward, but I do think its wise not to invite problems so I suggest avoid doing it.