Indeed. If you ever get the chance to see the film Lacho Drom do so. The film makers went all around the world filming Gypsies from all over making music. While there is definitely a common thread that goes though all the music, in general each group of Gypsies’ music had clear regional sounds. Indian, Arabic, Eastern European, etc…
I think when most people in the West talk about Gypsy music they are talking about some form of Eastern European music. The group Golden Bough does some stuff that could be classified as Gypsy sounding, and Margie Butler does some nice stuff with some of it on harp as part of the group. You may want to check out some of their recordings for ideas.