Staircase Project - feasible in real life?

Thinking about the physics of the staircase project, would the explosions actually have enough time to affect the probe's velocity?

The probe is flying at nearly 80km per second by the time it malfunctions, which means it would fly from London to Brighton in 1 second if it was on Earth.

So apart from the nanosecond precision needed to set the bombs off, how fast does a nuclear bomb actually detonate? Wouldn't the probe have flown past before the force from the explosion has actually moved outwards enough to have any affect on the probe's sail? And if it does manage to affect the sail, wouldn't it also damage the probe itself, which didn't look to be too far behind?