No, the paradox as described in the Wikipedia article doesn't assume the infinite level of sensitivity.
The figure explains it visually - the further away you go from the observer, the more stars you capture in your camera's field of view and the apparent brightness stays the same. The 1/r^2 term for light intensity is cancelled by the r^2 for the number of stars.
It's interesting think what an experimental result you describe would imply. It either contradicts the nature of light or that we're in the center of a cloud of stars where the density of stars falls with distance from us.