Is it technically possible to make someone see something when their eyes are closed?
Yes, this is most certainly possible and already being done. As long as the visual cortex of the brain (in the occipital lobe, i.e. at the back of your head) is functional, the correct stimulation will produce visual perception.

In cases of blindness caused by malfunction of the retina, meaning that the rest of the visual pathway is functional, this is the most promising approach to restoring vision. See Visual prosthesis and the TED talk on it.

"Virtual vision" as in projecting a whole field of vision (reflecting the real surroundings) is the big ideal target that this technology is aiming for. Of course as soon as they manage to make a working prosthesis for blind people, someone will probably try to make it non-invasive and easily usable for commercial exploitation.