My understanding is that the eyes are actually quite poor in terms of providing the brain with a clean image. Perhaps the only areas where eyes are better than cameras are with simultaneously viewing light and dark together (high-contrast), being quite fast at focusing, and being able to see reasonably in low-light. Each eye has a full-on blind spot, and the ability to see colours in the periphery is quite limited. Almost everything about our clean visual perception is a result of the brain's compensatory mechanisms -- such as filling in holes and choosing colours based on memories.
Although an unscientific perspective, when I dream, I can see clearly not only in the centre but also in my periphery. Moreover, my vision does not have the static-like overlay in my dreams like it does in real life. (I am often consciously aware when I am dreaming, wherein I have done various tests in my dreams) Hence, my guess is that the brain is capable of handling a fair bit more data than the eyes provide.
When you consider all the people born with abnormalities, and when you consider the array of change that your body goes through during development all the way through old age, it should be capable of handling all sorts of unnatural situations. Even looking at a computer screen and understanding the idea of windows being behind other windows and the idea of a webpage being like a long scroll for which you can see only a part of it are rather unnatural. Many of those brought up before the time of computers have a great deal of difficulty understanding the virtual realm that resides inside the screen (of computers, smartphones, and other modern gadgets).
The concentration of receptors is vastly greater near the centre of visual fixation. While I doubt the brain could handle seeing in full definition in the periphery, it could probably handle quite a bit more than it currently does. I do believe the brain could handle mentally focusing on multiple regions simultaneously. I can focus mentally on three or four areas of my periphery at once, despite the image being quite unclear. At the same time, the brain has limited capacity. For example, they say that the human brain can handle tracking up to 60 moving objects within something like 30deg of visual field. If we could see all the way around us at once, I imagine it would be quite demanding of our attention -- but I am sure we could grow to become accustomed to it.