I personally wouldn't have the smoke raise like that, I feel it looks too choppy and fake. I would, however have the smoke there after the explosion occurs, when the player regains consciousness.
Here's a script of how I would do it:
1) Player is walking around, sounds are playing indicating nuclear attack.
2) Camera shake, panicky breathing. Loud sound of explosion. Bloom on everything goes extremely high, which then causes the players screen to go 100% white.
3) White fades out to black, giving the feeling of unconsciousness.
4) Player returns seeing a semi-transparent mushroom cloud in the distance. Walking is restricted to a slower pace. Breathing and radio are in background. "Painful Eye" hud is displayed, giving the feeling of shock/slow motion.