If one is to postulate an entity that has a complete or absolute lack of height, depth, and width, can such an entity be located anywhere? Or does attribution of location to an entity entail length, depth, or width (assuming a three-dimensional world)?
David Gudeman rightly points out that your entity is called a point. A point by definition has no extension. How that is possible is that Euclidean space is concerned with having dimensions that are mapped to a real sequence. Thus, a point can have a triple that describes it's location (x,y,z) even though it has no length, breadth, or height ([x1,x2],[y1,y2], [z1,z2]). In more advanced models of space, points can have more complex definitions other than no extension or ranges.
Judging by your response to JD's excellent answer, what you seem to be asking is whether it makes any sense to talk about an unreal object having a location. I think the answer is generally no, it doesn't. Incidentally, even objects which we do consider to be real and to have a finite extent, such as electrons, don't always have a well-defined location, since according to quantum theory their position is essentially a matter of probabilities. That all said, there is one type of non-physical object, namely a point in space, which we imagine expressly for the purpose of allocating a location to it. If you are struggling to come to terms with that idea, imagine that we use a small sphere to mark a position in space. Presumably you are OK with that idea, because a sphere has a length, breadth and depth. But how do you allocate a location to a sphere? Conventionally, we do so by associating coordinates with its centre. Its centre is a point that has no length, breadth or depth, yet you should be able to feel Ok giving it a definite location in space because you are happy with the idea of the surrounding sphere being a real object.
In a three-dimensional world, location is defined as a point that is represented by 3 numbers; one for each dimension; ex. height, depth, and width. So, if an entity does not have height, depth, and width, it cannot be represented in a three-dimensional world, which means that location cannot be assigned to it.