It was not handheld. It weighed over 300 hundred pounds, maybe as much as a tonne. The connection between the barrels and the main box must have been structural, though active and flexible - "a wrist-thick bundle of black tubes and cables" is all he says about that.
It made so many holes that it destroyed the structural integrity of the boat, and the unsupported upper bits started collapsing due to their own weight. The rounds are 0.3mm wide and lets say we need 1km of holes - that's 3.33e6 rounds. If the rounds are 2mm long cylinders made out of uranium, that's exactly 9kg of ammo. Over ten kilometers worth of holes would be possible. This thing was like a waterjet, but using uranium moving at a substantial fraction of orbital velocity.
The power is not impossible given that it's nuclear-powered and is using the ocean as a heat sink. If the rounds are moving at 5km/s and firing 27kg per minute, that's 5.6MW.
Given those numbers, the force is 2250N = 506 lbf. There are four guys, some equipment and supplies and this super-weapon on the raft. It's likely an under-estimate, but let's say 1250 lbs. That's 4m/s acceleration, 0.4 gravity. That would get them up to 23 knots in 3 seconds, if there were no drag. But there is a lot of drag, it's a raft. Just like in the book, they'll move away quickly, but the acceleration will fall off quickly, too. When firing stops, they'll slow down quickly.
Yes, it's extreme. That's the whole point. But it isn't physically impossible.