What happens if a tire goes flat while I am in a fast turn?
It depends on which tire, but the essential thing is a flat tire has almost no grip.

Two examples:


Two days ago I was descending a little hill at 60 kph (about 35 mph) when the rear tire suddenly went flat. Moving my weight forward as much as possible, I was able to maintain control while stopping using only the front brake. Turns were perilous, because the rear tire, had almost no grip, and kept trying to slide out. 
A few years ago I set out on a ride, and foolishly had not checked the tire pressures. The front tire had a slow leak and was at half it's normal pressure, which I discovered when attempting a high speed downhill off-camber turn. With barely any front grip, the bike went almost straight on. If there had been oncoming traffic then I would have hit it. 


As for the front tire coming off the rim, several years ago I was in a bunch and some of the bunch were swerving around in the buildup to a sprint. To avoid crossing wheels with the guy coming across me (who happened to be my brother) I had to turn sharply. We were doing about 35 kph at the time, and the cornering force rolled the tub off the rim. If you think it through, losing grip on the road is nothing compared to what happens when the tire that is now not on the rim gets to the top of the forks. The wheel stops rotating. So I was suddenly flying through the air, sans bike.

To answer your question how likely are you to die? Yes it's possible you'll die, if you hit a rock, tree, or oncoming traffic. That possibility depends somewhat on your bike control skills, and also on luck. But it also depends on where you choose to ride and in what manner. Hairy descents are not for busy roads.