We would have reached the conclusion that Earth isn't flat much more quickly.
http://www.lhup.edu/~dsimanek/flat/flateart.htm
As per this website (and what I can remember) the first evidence that the earth isn't flat came from the way ships disappeared as they got far away.
I guess some ancient cultures may have seen the shadow of the top of the earth on the ring looking round, but they might just as easily have come to the conclusion that as you go up north (or down south) you get to a big mountain (Mount Olympus maybe)?