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.