From Madras, this morning, comes my favorite search query of all time. You know, I am still getting around to this, so please don't consider the following as definitive.
Depends on what you mean by "element." In strictest vaastu practice, we are concerned with Earth, Water, Air, Fire, and Space: bhumi, jal, vayu, agni, aakash. Cross-culturally, I suppose you could say the turtle plays a role. In Chinese practice, this would primarily refer to a direction, i.e. north, rather than an element, although some people might want to associate the turtle with water. In Tibetan practice, "turtle features" are regarded both positively or negatively, usually depending on the purpose of the exercise.
I'll have to ask my friend Huang Ba Danh for more turtle information, and get back to you.