Not really-really.
There is only one official language, Italian and 12 minorities which cultures and languages are officially "protected" or "safeguarded".
That is the essence of the Law 482/99 you cited.
In two border regions (namely Trentino Alto Adige for German and Val d'Aosta for French) the population speaking the "other" language is so vast that there are special provisions that make those regions "bilingual", but in Friuli Slovenian is spoken by a minority and has much less relevance.
Albanian, Catalan, Greek, etc. are spoken by very small commmunities (still coming from the original country where the language is spoken) that "immigrated" in Italy centuries ago, and often they diverge from the "original".
Sardinian is instead a "self-standing dialect", a local historical language of the island, that is "protected", but nothing more (you don't have official state documents written in Sardinian, nor official signs, etc.).
The "tower of babel" (that was a problem in the past) did not came however from those "foreign" languages, after all Italy has century old tradition of trading with France, Germany, etc., but rather from the dialects, and from the lack of schooling/education.
Dialects are local and independent from other European languages (though of course they may well have been influenced from them (take the dialects of Sicily as an example) you can find in it words that clearly come from Spanish or French (or even Arabic).
The people that immigrated to the US obviously largely came from the poorest (and most isolated) regions and the dialect they spoke had very little in common with Italian, a large number of those people couldn't read or write (at least not properly) in Italian and for tens of years, they had no or little contacts with Italy, it is only too normal that words changed in the meantime.