Yes, exactly that snake from the Rod of Asclepius! :) After getting to know one of them personally, I understand why they were chosen as a part of the symbol of healing and medicine. Compared to the other snake species that lived on our land -mostly adders and grass snakes- Aesculapians behave noticeably calmer around humans, don't panic easily and are non aggressive. Because of that, to me as a kid they seemed special and even friendly in a way. At the same time I was afraid of all the other snakes, when I occasionally met them on my way home from school. That was despite the fact that Aeskulaps grow to a much bigger size than the other snakes in that biome. An old village lady told me then that you can even tame them by placing a saucer of milk on the veranda and sitting a little closer to the feeding snake every evening. I never even considered doing that though, had way too much respect for the animal.

In contact with humans, they can be rather tame, possibly due to their cryptic coloration keeping them hidden within their natural environment. They usually disappear and hide, but if cornered they may sometimes stand their ground and try to intimidate their opponent, sometimes with a chewing-like movement of the mouth and occasionally biting.

The English wiki article on them is quite interesting.