The thickness of the vinyl and the backing color (clear or gray) will make a difference in illumination. It will tend to look a little washed out but should have some illumination qualities. I do have backlit translite material that may be the most beneficial for you as it's meant to be illuminated from behind. It is free floating (no adhesive) so you would want to find a way to secure it in place. If you simply stretch your side art vinyl over the hole you should notice some illumination but again, it may look washed out or faded.
If you would like more info on this send me a PM and I can follow up with you later tonight or at some point tomorrow.