Simple question but the keywords involved made Googling fruitless.
I'm just curious if the back camera on an iOS device can be recording/streaming video while the display is used for something other than a viewfinder.
The answer is absolutely.
You can hide your capture/video view as the other answer suggests, but assuming that you already have permission to use video (and/or audio if it's an AV stream), you can do whatever you want.
Granted, I'd stick to "don't be evil" as your shtick, as one of the important, but purposefully vague app store submission guidelines is simply "they know something is wrong when they see it."
See my answer here for a very related question & answer.