Now obviously the shaft here functioned nearly like a gun barrel so the manhole cover could've reached 5-6x the escape velocity (according to the scientists), but even just being accelerated to 10% of escape velocity in the span of milliseconds would've turned the hapless Mr. Jones into a fine red paste. Assuming he resided in a metal fridge at the time, he would've become what can only be described as a flat tin can of pâté.
Edit: And before anyone mentions the fact that Brownlee's calculation did not take into consideration atmospheric forces (which probably disintegrated the cap before it got to space), at least some molecules of the cap probably did go that far, and would still remain the fastest, and possibly furthest object from Earth (assuming it did not get caught in the gravity well of another object on its way out).
There have been objects placed even closer to nukes that have survived and note Project Orion--not only objects near a bomb, but the plan was to put a crew near bombs. Obviously, they would catch some radiation but that's going to happen anyway in deep space flight and back then they didn't realize the cancer risk.
The basic physics of protecting the ship and crew from the nearby detonations is clear. There is some question about whether it could actually be used to take off from Earth, though--it's not so certain if the pusher plate could be kept cool enough during the ride to orbit. Deep space doesn't require such sustained thrust, it's no problem. EMP from near-Earth detonations is a big issue, though.