Nope, there are many studies showing that the "flood" of people from different areas did not alter significantly the genetic composition of the Italian populaceThis is not true, pre-Roman expansion Italy is very different from post-Roman expansion Italy, the peninsular was virtually flooded with Easter Mediterranean populations, especially urban areas.
https://ilsizzi.wordpress.com/2016/07/14/la-struttura-genetica-degli-italiani/
(Could not find a source in ENglish, my apologies).