I came across a possible explanation as to why the rabbis would insert this brief tid bit about Nero converting to Judaism into the narrative (if it wasn't factual -- if there are sources supporting that his conversion was factual, please do list -- that would be interesting)!
In Jeffrey Rubenstein's "Talmudic Stories: Narrative Art, Composition, and Culture," he dedicates an entire chapter to Gittin 55b-56b. He theorizes that not only does this passage deal with the obvious destruction of Jerusalem, but with the Rabbinic Authority. Throughout the passage, we see how the sages' inability to decide due to being too cautious leads to destruction.
Rubenstein posits that Nero's presence is to serve as a stark contrast to the sages. Like the sages, Nero displays caution by soliciting an oracle that his imperial commission to attack Jerusalem meets divine approval (the four arrows falling towards Jerusalem). He sought additional confirmation – by consulting the child and having him rehearse a scripture, which details the destruction of Jerusalem.
Nero, like the sages, faces a difficult decision (the rabbis had previously faced a difficult decision on how to react to a host treating an unwanted guest at a banquet as well as how to handle the emperor's blemished calf he personally offered). Nero acts by not destroying Jerusalem by fleeing and converting to Judaism, thereby avoiding the clutches of the emperor, demonstrating his faith in the God of Israel and siding with the ultimate victor.
It is here that Rubenstein explains this antedote: "The strange/nonhistorical account functions as an ironic foil with which to compare the behavior of the sages. When pressed to act by the emperor, they do not seek omens, or inquire of children, or turn to the text themselves. Nero – the Roman – the pagan, the goy – does... Nero’s courage produces a rabbinic authority and the proliferation of Torah; rabbinic cowardice leads to the destruction of Jerusalem."
Essentially, according to Rubenstein, the Nero scene is an ironic "slap-in-the-face" to the sages, who failed to act, because even the wicked pagan Nero knew to seek counsel from a higher being, etc.
Now this is Rubenstein's interpretation. I would be interested to know what other interpretations are out there (and if there are supporting evidences for Nero's conversion).