Yes, single atoms do cast shadows! This has been understood for about 100 years but was only demonstrated experimentally recently, in this paper from 2012.
On the scale of things smaller than the wavelength of light, the shadow in the far field will never be smaller than the diffraction limit. Instead of a sharp outline that you see with macroscopic objects, the diffraction pattern formed by the shadow is a smooth function determined by the optics of the microscope.
Everything is partially transparent at this small scale as well, so the intensity of the shadow is determined by how much light the object can absorb. For individual atoms, the absorption is only significant at very narrow peaks in wavelength. So you need to be sure to tune your light source right at one of these peaks to get a decent shadow.
In the paper above, the authors trapped a single, laser-cooled ytterbium ion and used a light source tuned to a peak around 369.5 nm. That means they were imaging in UV, but in principle this approach could work with visible light as well. The final image showed about a 3% decrease in intensity at the center of the shadow. The wavelength of light used to illuminate the atom had to be precise to about one part per billion or the shadow disappeared.