OK I have calculated the time needed for bronze and it seems that we willget it in 6 turns regardless of whether Natives save gold from third turn.
Of course the overflow to archery will be less so we will get archery 1 turn later.
So in the cost of delaying archery...and every other tech after that for 1 turn, natives will get a chance to upgrade a warrior to a dog and cause some damage or at least slow down significantly his closest civ (if there is one).
It is a gamble...it might pay off or not...what do you say?