This is almost definitely the most accurate way to simulate assimilation.
Public education was originally advocated in the United States as a reaction to increasing immigration. And it worked, too- within a generation, in almost all respects immigrants were inarguably American. While most retained their religion (Jews and Catholics) and some cultural discrepancies (foods, phrases), they became indoctrinated with Americanism. You can really see this visiting a Little Italy or Chinatown- while architecture, food and people will reflect that of Italy or China, American overtones will abound (and did in the past), and loyalties were to the United States rather than the immigrants' native nations.
This DID matter in the Old World, too. More than a million Frenchmen are of Polish descent. Ashkenazic Jews from Eastern Europe migrated in large numbers to France, England, and the Netherlands. There are not large population of Yiddish or Polish speakers in these nations- loyalties were changed, mostly through public education.
Of course this didn't work as well with resident minorities. Those who immigrated were in a much different position- thrust into a new society, rather than having resisted it for generations. That's why something I'd love to see is the "Resident Minority"- maybe tagging each pop which is a minority that should stay, such as the blacks in the the US South or the Germans in France, or designating the entire culture so it will not assimilate (as it often did, inaccurately and annoyingly, in Vic 1).