Its an accident waiting to happen.
Many years ago, I had the most horrifying thing happen to me: a drive shaft (chevy) fell out of the transmission, and not only banged on the road, but also on the floor of the car, with me almost getting a heart attack (try to imagine the noise and "earthquake" at the same time). The car was not mine, and I just got into it, so there was no time even to notice that something was off. Luckily this happened while I was just accelerating, doing maybe 10-20 mph, but I hate to think what would happen at highway speed...
Seriously, I've been through all kinds of things, in cars (usually not mine), but that incident takes the cake.
As for vibrations, it seems that on our 1st gen LS, the differential mounts/bushings whatever they are called were no good to start with. There should be three of them and I believe there was even a SB for that. The problem should be similar to bad transmission and engine mounts, with possible noise too. I am planning on checking mine, but they say it is hard to see if they are good or not - possibly one way would be to put it in drive, and get the wheels against something so that car cannot move and then look under the car to see if the rubber is cracked. Who wants to go under a car while it is in drive?