Could they have taken the aircraft into the air after having the flight control unlocked ?
The Gust Lock is operated from the cockpit, via a lever near the flap handle. However, the gust lock
cannot be disengaged if the Flight Power hydraulic assist system is already loading on the flight controls.
So normally the gust lock must be released early in the checklist, when the hydraulic system still unpressurized before the engine is started. Otherwise the gust lock will remain engaged until the engines are shut off again and hydraulic pressure is removed.
There is a Flight Power Shut-off Valve (FPSOV) which can be pulled in an emergency in case there is a jam in the hydraulic system. The FPSOV will relieve the hydraulic pressure. It can also be used as an unapproved way to disengage the gust lock once engines have been started (e.g., during taxi).
There's evidence that the crew pulled the FPSOV. But, it is not known if pulling the FPSOV during a take-off run will successfully disengage the gust lock, because now we're dealing with aerodynamic pressures loading on the flight controls, in addition to the hydraulic pressure.
"the pilot in command indicated that the flight controls were locked, but the crew did not begin to apply the brakes for another 10 seconds and did not reduce engine power until four more seconds had passed."
My guess it that despite the recorded comment, somehow internally there was some combination of disbelief and of "success orientation", but that is a pretty wild guess.
Part of the reason is that they did not discover the issue until after v1, when they attempted to rotate. Pilots are trained with the mindset that problems before v1 == rejected take-off, while anything > v1 means continuing the flight.
Another reason is they might have initially thought that they were having a power hydraulics issue and so they tried to solve it by pulling on the FPSOV handle (as above) and tugging on the flight controls.