I would imagine that meatballs in "Italian" cuisine have a longer history then that, as the Roman gastronome Apicus in the first century AD included a number of recipes for "meat balls'.I would speculate that early contact with a country like turkey, whose cuisine boasts almost 100 variations on "Kofta" to be the likely entry point of the style of dumpling. As to it's popularity...well I don't think the humble meatball needed the same dictums as say potatoes or other nightshades and new world foods(as they are not biblically mentioned,hence the church bans) to bring to popular use...

a side note about Albondigas- During the Inquisition Albondigas were made with a combination of Pork and other ground meats, and served at table to "out' 'conversi'-those Jews that were secretly hiding out as converts to avoid persecution but who were still practicing Kosher law. Albondigas(sans puerco) being a common food for the Sephardic Jews whose own origins were closer to the Moors thenthe catholic Spanish. When the Inquisition spread to the new world...in fact the inquisition somewhat responsible for the early Colombian and post Colombian settlements, and later set up shop in Mexico, the humble albondiga was used as proof for persecution by the The Inquisition in Mexico of Judaizers. if they refused to eat or spit it out when informed of its contents they were arrested.