The short answer: No.

Snopes has a recent entry debunking this myth. The author of the piece looked at one of the popular e-mail forwards where someone claimed they’d read about aspartame being developed as an ant poison. This person then explained how she’d used aspartame to fight off ants and that it was an effective deterrent. 

So the Snopes team decided to test this claim:

As a test, we conducted a simple experiment by setting up three Ant Farm brand live ant habitats and stocking them with harvester ants. The ants of one habitat were fed (refined) sugar, sugar water, and products made with sugar; the ants of another habitat were fed aspartame, Diet Coke, and products made with aspartame; and the ants of a control group were fed ordinary water and the types of (natural) foods recommended by the Ant Farm manufacturers. The ants that were fed aspartame not only survived but thrived, digging as many tunnels and appearing just as active as their counterparts from the other two habitats

There’s a brief explanation in the article about how the myth likely got started. There was no discussion about whether the atomic bomb was originally developed to rid the South of fire ants.