No, he died because of a steering column failure, not a loss of downforce.
Edit: I read up some more and it seems that noone really knows why he lost control. My previous impression was that the steering column broke mid-corner causing him to crash into the wall.
This is from an interview with Adrian Newey who designed the car:
Newey admits that he has considered the causes of the crash repeatedly over the past 17 years. "If you look at the camera shots, especially from Michael Schumacher's following car, the car didn't understeer off the track. It oversteered which is not consistent with a steering column failure. The rear of the car stepped out and all the data suggests that happened. Ayrton then corrected that by going to 50% throttle which would be consistent with trying to reduce the rear stepping out and then, half-a-second later, he went hard on the brakes. The question then is why did the rear step out? The car bottomed much harder on that second lap which again appears to be unusual because the tyre pressure should have come up by then – which leaves you expecting that the right rear tyre probably picked up a puncture from debris on the track. If I was pushed into picking out a single most likely cause that would be it."
