None actually had expansion tanks- up to 1973 model year when 'everything' changed.
Basic rules of thumb-
1) No Corvette prior to 1973 had a true 'overflow' tank, but some had a pressurized surge or external expansion tank (two different names for the same barrel shaped aluminum tank on the inner fender well)
2) If the car originally had a radiator with a filler cap on it, there was no need for a surge or external expansion tank as there was provision for expansion of the coolant internally to the radiator. These radiators are usually brass/copper construction
3) If the original radiator had no filler cap, then a surge or external expansion tank was required. The radiator had no room for expansion internally as it ran 100% full all the time. These radiators are usually of aluminum construction.
4) It's a common mistake to run either configuration above filled to capacity as the excess coolant will puke on the ground shortly after shutdown. This puking is not a sign of malfunction, the system just needs a certain amount of air space for expansion.
5) In 1973 GM introduced a true coolant recovery tank system on the Corvette. This is the white plastic non-pressurized tank mounted on the right inner fender well. All cars had a radiator with a filler cap and were designed to be filled to the top. Once the coolant expanded and reached the set running pressure, the excess coolant was allowed to vent into the expansion tank. After shut down, the coolant was sucked back into the radiator. No puking.
The only thing that puzzles me is why it took GM so long to introduce this system as it's far superior to it's predecessors.
The trick is to determine which type of radiator is original and correct for your car. It varies quite a bit even within a given model year.