Yes. Elves and mortals are said to be one people, and yet there are significant differences. We aren't actually immortal, but we age only very slowly, and we don't give up our bodies easily. Elves were created to love the earth, and our spirits have much influence over the material. We can be injured or killed, but we don't get sick. Our sages say that because we don't ever leave the Earth, whether we live or die, we were granted a vast resistance to things that can afflict or even kill a mortal. That includes disease.

[ Elvish Philosophy 101. XD ]