Civ II : I remember being able to cash rush from turn 1.
Yes, Civ V eliminated the discount for partially constructed buildings / units that had been there from the beginning. (That decision was made during development; as a consequence they turned off the AI cash buying of buildings to keep AI from wasting cash). However I do note that prior to Civ V, you still had to wait for your next turn for the building / unit. In Civ V, you can cash rush multiple buildings in the same city the same turn.