Yes, UV rays cause damage to pretty much any organic matter, that's the reason we wear sunscreen, sunglasses, and why cheap "fake" sunglasses can be harmful for your eyes (the glass is simply tinted and does not filter out the UVs, which is what they should be doing)

edit: the way I remember it is that like any type of radiation, anything that goes into your body stays there pretty much until your death, the only way to keep your "uv capital" in good shape is to be proactive about it, cant do anything retroactively. This is why about 1/3rd of Australians will develop some form of skin cancer in their lifetime.