Is it possible for two people to repopulate earth?
Well, mathematically it might be possible. But, I would rather worry about the low amount of genetic diversity that the growing population would have, which would make it extremely sensitive to external stresses.

To repopulate earth from such a small pool of genetic material, one would need an organism that is much more sturdy as compared to humans in extreme conditions, multiplies fast and is much more prone to mutations that actually convert to a phenotypic significance so as to increase the genetic diversity of the total population.