It kind of did. During the Roman Republic, the south was way more developed. This was a reality even before Roman rule. Southern Italy was colonized by multiple Greek cities, and cities like Tarentum or Syracuse reached great status and wealth. The Romans called this collection of wealthy cities the "Magna Graecia" (in English: The Grand Greece, a name which also tells us how Greek these cities were, because they were considered an extension of Greece itself). Meanwhile, the north was barbaric and, excepting the Etruscan cities (which couldn't compete with the Greek ones in terms of economy), very poor. In fact, northern Italy was colonized by the Gauls, which used the region to invade the rest of Italy from time to time (even Rome was once sacked by them).

When time passed and Rome turned into the Empire, the divide wasn't so obvious. Italy as a whole benefitted from the imperial status of Rome and so development happened all over the peninsula. However, the south was still greatly developed and therefore richer because of its past and the commerce, that flourished because of the Pax Romana. The city of Pompeii, famously destroyed by the eruption of the Vesuvius, was an example of the rich and developed cities of the south, full of villas, taverns, wine plantations and all sorts of luxuries.

This continued to be true until the decline of the Empire. The north was ravaged by barbarians in the coming centuries, and therefore northern Italy was severely damaged (with the exceptions of the greatly fortified cities of Milan and Ravenna), while the south, not so close to the Empire's borders, maintained a higher status, although later on not even them would escape from barbarian attacks (let us remember that the Vandals stayed in the south for a little).

Generally, in conclusion, there was a divide. However, ironically, the south was more economically powerful (well, they were more powerful in general). As you may have found already, in the future the invasions would come from the south, not from the north, so the northern cities like Venice, Florence or Genova, once ravaged by war, would end up becoming the more powerful half, a situation that keeps going on today.