I was reading an article that quoted a surgeon who works on these types of injuries and his take was that it would be quick but not impossible, and the risk would not really be hurting the Achilles again but hurting something else in the knee, ankle or leg trying to compensate for it.
Apparently there was a Russian gymnast who competed in the Olympics just 3 months after tearing his achilles, and of course a gymnast is landing on it, exploding off of it, putting a ton more force on it than a QB.