When you draw, do you find yourself kind of 'feeling out' what you're drawing, as if you have a perception of the depth of the object?
It depends. A drawing professor once told me that skilled draftspeople look more at the subject than they do at their work, and when you do that, you are feeling along the contours of the thing with your eye as you replicate them with your hand. But at the same time If I’m drawing from life, or from a preexisting image, the process requires discarding intellectual information about the thing being drawn: you draw only what you actually see, not what you understand to be there. In that sense the depth of the object doesn’t matter, only the two-dimensional lines and shadows which the depth produces.
If I’m drawing from my imagination the process is a little different. Sometimes I’m kind of 3D rendering it in my mind in order to get the shading and foreshortening right, but years of consistent life drawing practice mean that I’ve more or less memorized convincing configurations of lines for thousands of frequently-drawn objects, and I usually don’t have to think it through that much.