Literary: The imagery of the ripe harvest and the sickle comes from the Bible rather than the Mesoamerican experience. For a literary touchstone, Joseph might have taken this imagery from either Joel or the book of Revelations:
Joel 3:13 Put ye in the sickle, for the harvest is ripe: come, get you down; for the press is full, the fats overflow; for their wickedness is great.
Revelation 14:15-18 And another angel came out of the temple, crying with a loud voice to him that sat on the cloud, Thrust in thy sickle, and reap: for the time is come for thee to reap; for the harvest of the earth is ripe.
16 And he that sat on the cloud thrust in his sickle on the earth; and the earth was reaped.
17 And another angel came out of the temple which is in heaven, he also having a sharp sickle.
18 And another angel came out from the altar, which had power over fire; and cried with a loud cry to him that had the sharp sickle, saying, Thrust in thy sharp sickle, and gather the clusters of the vine of the earth; for her grapes are fully ripe.
The imagery of the ripe field being reaped with a sickle was natural in the Old World, and probably to Joseph on the American frontier. It would not, however, be the appropriate imagery for Mesoamerica. This is not because of the ripened fields, for surely there were ripened fields, and indigenous Mesoamerican imagery is full if the import of ripening foodstuffs. The difference is the sickle.
The sickle is an instrument for harvesting grains that grown on long flexible stalks. The principal grains of the New World would not have fit that description, and it is quite doubtful that anyone would have an image of harvesting corn with a sickle, as a straight bladed instrument would be quite sufficient.
None of this suggests that the absence of a sickle in Mesoamerican says anything except that Joseph’s use of the term is influenced more by the language of the Bible than by the particular imagery that might have been on the plates. Of course it is possible that Ammon used a specific reference to Joel, but it is more likely that the original imagery would have been more specific to the ripening/harvesting images with which he and his brethren would have been most familiar. Of course this same imagery appears in D&C 4:4.