Without actually hearing what you are describing, I would say that the noise you are hearing is the normal rattle that accompanies a normal take-off from a standstill. The transmission on the C5 is in the rear, the driveshaft comes directly from the clutch and goes back to the transmission, V.S. a conventional clutch/transmission setup where the transmission pilot shaft is splined directly to the clutch disc. Therefore, in the Corvette as the clutch is engaged to get the car rolling, the driveshaft recieves the engine impulses and clutch disk vibrations directly, instead of being fed through the transmission gear train. This vibration so to speak, is amplified by the drivetrain as an audible rattle, and probably further amplified through the torque tube like a hollow drum, which in essence is all the torque tube really is.
The clunking that you refer to also sounds like the normal engagement clunk, the shift rod goes from just below the shifter all the way back to the transmission, that's just about even with the back of the seats, long in terms of shifter linkage.
Also, something you can do that really brings home the spinning mass of the rear transmission driveshaft design; with your engine at an idle, let the clutch out with the transmission in neutral, hear the rattle sound, now depress the clutch, and quickly place the gear shift in 1st, keeping the clutch depressed, feel the car move forward slightly. That's the energy of the spinning mass of the driveshaft moving the car as you engage 1st gear. It probably works in any gear, but I used first for this example. Now imagine how much rotating energy is present when the RPM is up higher than an idle, say 6500 RPM. Gives one much more appreciation for the effort those blocker rings and syncros are performing during gear changes doesn't it?
One last word about having a mechanic check your car for normal operation. Make certain the mech/tech is very familiar with the C5 design Corvette. Old trains of thought may cause concern for what should be considered normal drivetrain noise and normal system(s) operation.
One more item that was just brought up, the torque tube. The torque tube is actually a structual component, it is bolted to the rear of the bellhousing and the front of the transmission. It doesn't rotate, but actually "ties" the engine to the rear transmission, thus producing a very rigid structure. The rotating driveshaft is located inside the torque tube. Re. whoever said the torque tube would rust and eventually fail, THAT'S an example of what I was saying about making certain the your mechanic/tech knows what is talking about.
Sure it might rust and fail, maybe in about 150 years.
vettepilot
I hit the replay button 30 minutes before I hit the submit button (distractions) and didn't see the previous replies. 
