I'm not aware of any genetic studies, no, but that doesn't really matter when discuasing ethnicity. Ethnicity, like race, is a purely cultural concept driven by mixture of actors ranging from language to self-identification. While genetics, especially phenotype can play a role, this is more to do with the way they are percieved within a community rather than any innate trait of genetics.

As such, the Yazidis are a distinct ethnoreligious group. Their cultural and traditions are quite unlike the Kurds and they practice endagomous marriage and kinship. They are almost exclusively of the Yazidi religion which is to them a key marker of identity, though some have converted to Islam but maintain a "Yazidi" identity. All of these mark them as a seperate ethnic group.

However, ethnicity is complicated and a person can have more than one and there can be sub-ethnicities within a large one. Furthermore, we have to look at what constitutes a nationality. A nation is a group of related people with the desire or ability to form a state. Now, we have tied our idea of nation and state very closely, but this was not always the case. Anyway, the Kurds constitute both a nation and an ethnicity, but have no state. They are not stateless however in the sense that they inhabit and are citizens of a number of different states.

I'm going into this because I think it is important to my next point. Yazidi's are Kurdish, but they are not necessarilly Kurds. Kurdish identity is very complicated and we aren't entirely sure of their history. If I recall correctly "Kurd" comes from the middle-Persian "Kwrt" meaning nomad and was broadly applied to a number of nomadic peoples. The group we now know as Kurds aren't mentioned in records until Islamic times. Their languages are Northwestern and are thus more closely related to Median and Parthian than Old Persian. As such, we can assume that some independent identity, at least in linguistic terms predates old Persian, however this might not mean much as language and culture are very fluid, so a person living in Persia but speaking a different language might still have thought of themselves as "Persian" rather than say "Parthian." That aside, by Islamic times, the Kurds had developed a distinct identity.

Like other groups that existed on the fringes of Islamic territory, their conversion to Islam was spotty, and those that did adopt Islam often mixed it with other practices. Just as it is hard to say when the Kurdish identity emerged, it is difficult to say exactly when a Yazidi identity emerged, but by the 11th century, they were identified as a group who venerated Caliph Yazīd to an unorthodox extent. By this time, wandering Sufis had gained enormous influence in the region. 'Adi ibn Musafir was among the most prominent and it his songs and poetry had a transformative effect on Yazidi religion. By the 15th century, Yazidi religion and culture was formalized.

Yazidi culture an religion is Iranian and Kurdish in origin, but has absorbed a wide variety of influences as well as its own spin on things. So while it is not untrue to say they are Kurds or Kurdish, it is only a part of a much greater picture and many feel very seperate from the Kurdish majority.