I agree with your statement above. I can think of reasons why no Moslem would want to claim genetic ties with Israel, I can think of propaganda reasons for both doing it and not doing it, and I can think of religious reasons why those related to Israel but who had converted to Islam would want to stand and proudly proclaim that they had done the right thing.
And like you mention, the war going on isn't gonna 'cause anyone to rush to the DNA clinic anytime soon.
Jews and Arabs have very nearly identical DNA signatures. They are much closer to each other than either is to any other group.