The drainage itself doesn't cause damage. If you leave the water for too long, you will damage the roots since they need oxygen, just like in hydroponics, where oxygen is added to the water using air pumps. What can also damage your roots is sunlight or LED light that reaches them if you use clear cups or bottles. You need to keep emptying the water and put them in something dark, or darken the bottles. Or do something to add oxygen to the water, cheers!