A full-sized plane would probably have some front-facing windows, but I'd expect most of the visual approach to be done by instruments anyway. In order to have a view of the runway during landing, the Concorde had an enormous and heavy movable nose.
Far more likely is that abrupt area changes cause discrete shocks, each of which could merge into the "sonic boom" that the demonstrator is designed to alleviate. However, a simpler way to understand it is that, from a practical point of view, you basically want to be flying a needle to reduce the boom to its minimum possible volume.
I would opt for much simpler camera, an already-proven ILS and windows that allow the pilot to look down on the side of the plane.
The fewer things to go wrong on a brand-new design, the better.