Raimey,

Champagne is a strictly protected brand already since the 19th century. This is recognized in about 130 countries around the world.

I believe that someone who wants to buy a H&H will always attach great importance to the fact that it also comes from England. Otherwise, his pleasure would be clouded to spend so much money on it.
However, it is conceivable that there will be certain "synergy" effects. For example, Beretta could supply the barrels or CNC milled systems. However, they will probably be very careful with this so as not to damage the reputation of the traditional brand.
In order to sell expensive and exclusive shotguns, Beretta did not have to buy H&H - they have been building quite outstanding luxury shotguns themselves for ages.
Beretta's purchasing policy so far also shows that they are very prudent with the brands they acquire.
Examples are Benelli, Sako and more recently Chapuis.
As I said, Beretta is certainly a more competent owner/partner than, say, Chanel or the Swiss holding company that owns Purdey.
I find it interesting that it is ultimately the Italians, often ridiculed in the past, who are driving a successful (survival) strategy. Who would have dreamed of this in Great Britain?

Cheers,
Wolfgang