Ha, interesting question. I would say that ultimately the representation we have of the world is always somehow a mathematical structure, even though we don't always realize that.
Now, one can consider your question on two levels. The first one is: are atomic models things we would *SEE* if we just could see such fine details ? There, the answer is simple: no. Because what we call "seeing" is an approximate intensity distribution of light on a surface (retina, photographic plate, CCD, ...), and such an intensity distribution doesn't make much sense on a resolution below the wavelength of light, which is of the scale of several hundreds of atom diameters. So there's no physical way in which we could actually see atoms with light. Ok, you might say, but what if we use "light" of a shorter wavelength (X-rays). Well, the funny thing is that you now get peculiar interactions between the atoms and the X-rays, which will give you "images" which are not faithful representations of the "geometrical picture" but things such as diffraction images. If you go to still shorter wavelengths, you will have "light" that will be so energetic that it will actually alter (damage) your atoms, like wanting to look at a painting using an automatic gun or something. So we have no optical direct means to "see" atoms.
There are other tricks which DO work better. Electron microscopy for instance. One can more or less "feel" an atom with a scanning electron microscope, but what this apparatus actually does is to measure electrical equipotential surfaces, not so much "visible pictures". In that respect however, one does "see" structures which ressemble the laboratory models of molecules somewhat (bubbles attached to one another).
On a deeper level, one should see these models as geometrical and visual aids to the description of a mathematical structure that is used in certain theories about atomic structure, which succeed in making a lot of good predictions of experimental results. So then, they are nothing but a visual mnemonic technique to help you deal with the mathematics.