Indeed. For a group that has been around as long as this one, admixture is a sure thing. I, for one, know this first hand. Although a Jew of European origins, my Y-chromosome is pure Celtic. Who knew? ;-)
The celts migrated to various parts of Europe, including Galicia ("land of the Celts") in southern Poland, which had a large Jewish population for hundreds of years.
I've been meaning to have my DNA tested for years. I have suspected Roma (gypsy) ancestry on the Polish side of my family for some time. If one took a DNA sample of the average Pole, they would probably find Celtic, Semitic, Roma, Armenian (Poland had a sizeable Armenian population that assimilated), Mongolian, and Tatar DNA.