No! There is a decent amount of drawing involved in UX / UI Product Design. However, the purpose is to develop or communicate ideas, and that can be done very simply – meaning, it doesn't take a great deal of artistic talent.
If you're going into UX design, you're probably wondering how many creative aspects you need to invest in. For one, it certainly helps to be creative. However, a common question is whether a prospective UX designer needs to know how to draw. The answer, succinctly put, is no.