Actually it was unflyable at just about any speed. The DC-10 slat system is cable actuated. A big drum in the center E&E bay drives cables that are attached to a series of actuators that move the slats. When the engine and pylon departed the aircraft it took the the slat drive cables for the left wing with them also. When that happened, aerodynamic forces essentially forced the left wing slats to the retracted position with the resultant loss of camber and thus lift. Couple that with the loss of thrust from the missing engine you have the uncontrollable roll to the left. There may and I say may have been a "sweet spot" airspeed where the the aircraft may have been controllable but with the time allotted to the crew I doubt they ever would have found it. As far as they knew, they were dealing with nothing more that an engine failure. I'm pretty sure as soon as the engine and pylon left the aircraft the roll commenced.
The crew of 191 was following company SOP for engine failure after takeoff, specifying climbout at V2 until obstacle clearance altitude is reached or 800AGL (whichever is higher). Granted, the crew had no idea of the damage the left wing had sustained following separation of the #1 engine. But at the time of failure past V1, as shown by the FDR, they were able to liftoff at V2+6, and accelerate to 172 kts (V2 +19) in a stable, 1100fpm climb, maintaining aircraft control with rudder and bank into the good engine; even with the damage to the left wing slats. V2 was 153kts. The crew began to slow from 172kts, down to 153kts, per their SOP. However due to the wing/slat damage, at 159 kts (V2+6) the left wing stalled and a left roll developed to which the crew could not recover with the low altitude, since they were not aware that 159 was the "new" VMC due to damage (nor is there any way they could've known that without a formal controllability check at altitude).
If the crew had been given the flexibility of not slowing and giving up any speed that they had attained.... when getting airborne in an engine out scenario, in VMC, where obstacle clearance is
not an issue..... especially when climbing out under control and with an 1100fpm climb; things would likely have been different. Whatever speed you have, you accept, so long as you can still climb and avoid obstacles.....speed
is life at this point. The crew followed the SOP they trained on, and sadly, that SOP killed them. Had the crew maintained the speed they had, the accident may possibly not have occurred. It's very likely that they could've continued climbout to a safe altitude to where they could perform their checklists, perform a controllability check of the jet, and vector back around for a safe two-engine landing. But alas, we will never know.
Following that accident, AA changed that SOP & checklist in an Operations Bulletin to make climbout for obstacle clearance to be V2+10 minimum if speed attained at time of failure is in excess of that, and if obstacle clearance is still required.