Fortunately for us, this wouldn't actually work that way. Rather, each of the individual satellites would have a different orbit so the image wouldn't remain consistent, but instead converge into a point and invert itself on the other side of the Earth before coming back together again and repeating this process until they start colliding with one another or decay into the atmosphere. That is, unless each "pixel" made constant adjustments throughout the orbit, which would be a colossal waste of fuel.

Disclaimer: this is based only on my intuition from 780+ hours of Kerbal Space Program. I am not a scientist and I've never studied orbital mechanics.