I don't think it would make much difference, Itally or USA.
I am growing Japanese cucumbers ,Chinese eggplants and Armenian cucumbers, Thai basils, Korean mints,...Vietnames culantro, lemon grass....

Actually the Barese melon/cucumber is different. It is actually a melon that when very young can be used as a cucumber. When the Barese is allowed to mature it can be used as a melon with a flavor similar to Honey Dew Melon but not as sweet.

Now that I have the vine growing I can offer that the vine is very thick at around 1 ½ inch thick. The fruit set is prolific and the vine will take over your trellis. I have a 5 foot wide by 10 foot tall bamboo trellis. Had I known that this cucumber/melon was this prolific I would have planted only 2. We find that it tastes better if picked very small and peeled. If picked late it can still be used as a cuke if the seeds are scraped out - like a melon this cuke/melon has hard seeds.

I got my seeds from Seeds of Italy if anyone is interested.

Here is a link that might be useful: Cucumber Barese info