From the (admittedly little) I've read about the Gypsies, an interest in them because of True-love's roots, and a friend who lived with Gypsies for a time, I wouldn't be surprised if the musical influences went, more often, the other way. See the point Tradsinger makes about the C&W singing.
Gypsies do seem to be adept at taking up the music of the countries through which they travel, and in which they sometimes settle, and improving on it. Some of the Gypsy feel may then feed back again.

Having said that, I have wondered for some time now if there is a connection between the English May Day milkmaids and the dance of the milkmaids and Krishna in India. Black Sal and Sara Kali (and little pieces of coloured cloth). If there are connections are they Gypsy connections?

One point about the Gypsies is that our understanding of them and their traditions, musical and otherwise, doesn't matter to them. They know exactly who they are and what it is that makes them Gypsy. They seem not to be the least bit interested in proving anything.
Cheers, Joy