They would probably understand the majority in Puglia/Naples. Sicily it depends. In my opinion Sicilian is more similar to regular Italian than Barese. For instance, in Italian "come here" you can typically say "vieni qua" or vieni qui. In Siclian, calabrese and a lot of Napolitan dialects, it is "veni ca". In Barese it is "vien a do" with do (pronounced like "dough") being borrowed from Greek. Some Neapolitans form the outer provinces of Campania also use do instead of ca, but as you can see it is very different from regular Italian. Heres another sentence, in English "come here and give me a glass of red wine." In Sicilian it would be something like "veni ca e dammi nu bicchieri di vinu russu". In Barese, "vien a do e damm nu bicchier' de mirre russ'." Pretty similar, and I think a normal Italian speaker might be able to identify vinu russu as vino Rosso, but a Sicilian or other Italian might be stumped by the "do" and "mirre" parts. The word mirre in barese comes from the old latin merum, which was a word for pure wine. Most latin cultures used the Latin word vinum as their basis for the word wine. (Spanish vino, Portuguese vinho, French vin) however Barese just picked a different word from Latin meaning almost the same thing.