Judging by Amaranth's vigorous appreciation of hot, humid, rainy weather here in summers in Canada (where we call it red-root pigweed) I would think you would have no problem. The species certainly does not like cool and frost, and the roots can be susceptible to rot if not free draining, so make sure that the growing container has holes in the bottom and is raised up to prevent accumulation around the base. Otherwise it is a tried and true reliable crop in many tropical-like areas.
Amaranth does cross breed with other wild varieties, so your volunteers may just be slightly different from what you are expecting. In any case, seed will likely be copious, and if the plants get mature enough plenty for grower and birds.