No. I believe that 1968 was the first year for stamping ID numbers on the engine and transmission.

 

No VIN on engine and trans until 1/1/1968.

 

The only important thing about matching up a '66 engine would be the block casting date, which should probably be from a few weeks to a few months prior to the build date of the car. There is also an engine assembly date code stamped at the front on a pad at the top of the block.