Plants and trees definitely react to negative stimuli - producing protective hormones and chemicals and releasing them into the air -- saying that, what part of hydroponics do you rip plants out of the ground?

I grow seedlings in small containers and then transplant -- there shouldn't be damage to the root system or any system - or if you're worried about it plant the seed directly in the hydroponic system. It will take extra care but can be done.

With a well-maintained hydroponic system the plants are getting all of the nutrients they need so should be quite happy there, actually.