I don't have an answer in terms of percentages, but I thought I could offer at least some insight I may have. Really cool question though, never really thought of this.
So two ways to go about this answer. For one, when you close your eyes you immediately can register so called alpha waves from an EEG (electroencephalography). This was actually how EEG was first discovered, it's the easiest brain oscillation we can capture through scalp potentials and see with our bare eyes. You find these alpha oscillations at occipital and parietal locations, and are slow waves (8-12Hz). If you compare an alert person in an awake state, and someone who is tired or even deep sleep, you see a difference in oscillatory activity, so more alert higher frequencies (gamma bursts >50Hz) versus asleep slow wave (theta, delta). I may be wrong and this, and someone do correct me if I am, but I would propose that high frequencies would indicate more neuronal activity, whereas low frequencies less so. There is of course a preference in neuronal populations to have a frequency they best oscillate at, so then maybe that hypothesis is out the door. In any case, as soon as you shut your eyes, you get these slower oscillations.
But even when your eyes are open and processing visual information, already 100ms later does that information get to other brain areas. So things like ERPs (event related potentials) have shown emotional differences in those waveforms already after 100, 200ms. This indicates that already the brain is processing that stimulus, not JUST the visual cortex.
At the same time though, that is only lower-tier visual cortex. Almost the entire back portion of our heads and part of the temporal lobes are all higher order processing. We are very unique among vertebrates for having so much of our brain devoted to visual processing. Most other mammals rely mostly on olfaction.
So taken together, I would say that just due to the amount of neuronal mass that is committed to processing visual information, yes a significant amount of the energy budget goes to vision. If you look at fMRI images, you can see the entire occipital cortex light up, only when viewing pictures, as well as other areas talking to the visual cortex.
Very cool question, I'm curious if someone has a more accurate prediction of just how much energy it takes for our camera to work!