Yes, water will damage a brad new tattoo. This is why you are told to place a layer of Vaseline or other thick lotion over the top of it when you shower for the first week or so.

When you get a tattoo it will scab up over the top and this scab will contain some ink. This is perfectly normal and some of it is going to slough off. However, if you get a scab wet it will become softer and come off before it's ready to. On a tattoo this will not only re-open the tiny, pinprick injuries, but will draw more ink to the surface.

This causes a tattoo to look paler or even to have splotchy, uncolored areas. Avoid getting new tattoos wet as much as possible and clearly follow the care instructions you should have been given.