I assume we are talking about the Ōshū Fujiwara whose reign ended in 1189 by the hands of Minamoto no Yoritomo (and his army).
The problem with this question is what is implied by "emishi clan":
The word emishi is not a “racial” thing—in other words, it doesn’t mean being of the Ezo or Ainu people—but referred to the people living in a certain region, especially the northeastern provinces of Mutsu and Dewa. It is a socio-cultural construct. For court nobles in Kyoto in the Heian period identification as emishi constituted a derogative way of referring to a person stemming from this region, which was perceived as peripheral and thus “uncivilized”: in other words, a “barbarian” (1). It is thus not surprising that Motohira and Hidehira, the second and third heads of the Ōshū Fujiwara, were referred to with corresponding terms in court records (2). But more interestingly, their ancestor Kiyohira, the first of the Ōshū Fujiwara, self-identified as both “tōi” and “fushū,” both words that referred to being emishi (3).
But if this meant that they were genetically different from the people in the capital (e.g., “Ainu” instead of “Japanese”), the answer is no, as examinations of their mummified physical remains (which still exist) have even shown (4).
Motohira, who is the founder of the Ōshū Fujiwara, is the son of a certain Fujiwara no Tsunekiyo and a daughter of the emishi-chieftain Abe no Yoritoki. Tsunekiyo, the forefather of the Ōshū Fujiwara, appears in the Mutsu waki, a fictionalized account depicting the Former Nine-Years War (1051-1062). Originally said to have been one of the housemen of Minamoto no Yoriyoshi, the general entrusted with the northeast by the court, he was executed for siding with his father-in-law against Yoriyoshi. Tsunekiyo can also be verified as a resident of Mutsu province in the year 1047 in records of the Kōfukuji, the religious centre (ujidera, "clan temple") of the Fujiwara lineage. We therefore have grounds to assume that the Ōshū Fujiwara were indeed (seen as) members of the Fujiwara, with the records stating Tsunekiyo being descended from Fujiwara no Hidesato (5). He possibly chose to marry into, and consequently side with, the Abe since allying himself with the most powerful house in Mutsu proved a means to secure his own position within the region (Tsunekiyo possibly was a former vice-governor who then chose to settle in the province and became a local warrior lord) (6).
In Japanese culture, clan-, or rather, uji-membership (e.g., being Fujiwara) is transmitted paternally upon birth and pretty much unalienable. Hence, the Ōshū Fujiwara are, genealogically speaking, of Fujiwara descent and by virtue of their being based in the far-off northeastern periphery of Japan also socio-culturally categorized as emishi. But neither bears any deeper implications pertaining to biology, genetics, ethnicity, or race.
I do hope that I have gauged the intent buried in your question (are we talking biology or culture) correctly. :)
Notes:
(1) Takahashi 2009, 2–3. Also Ōtō 2012, 14–16. There were numerous words to express this. Likewise, people also spoke of Japanese from the not-that-remote Kantō region as "Azuma ebisu."
(2) As per their mentions in diary entries of the Taiki (1153 9-14) and Gyokuyō (1170 5-27); cf. Takahashi 2009, 1.
(3) Takahashi 2009, 1. It may be because, after the conquest of the region by the Tenno-centered polity in the ninth century, the terminology also came to be applied to denoting a specific social status: that of a former "barbarian" being integrated into the civilized sphere of the court. The connotation of social identity that thus became part of the terminology may have influenced the choice of Motohira to refer to himself as such. I am not sure why, however, since I have nothing more than this mention available to work with; cf. Ōtō 2012, 14–16.
(4) Takahashi 2009 3–4.
(5) Kudō 2005, 106-107. Almost all provincial warriors claiming descendance from the Fujiwara are of Hidesato descent.
(6) cf. Kudō 2005, 106-107.
Works cited:
Kudō, Masaki. Hiraizumi e no michi: Kokufu Taga-jō, Isawa chinjufu, Hiraizumi Fujiwara-shi. Tokyo: Yūzankaku, 2005.
Ōtō, Osamu. Nihonjin no sei, myōji, namae: Jinmei ni kizamareta rekishi. Tokyo: Yoshikawa Kōbunkan, 2012.
Takahashi, Tomio. Ōshū Fujiwara-shi: Sono hikari to kage. Tokyo: Yoshikawa Kōbunkan, 2009.