The sitar has been used in jazz:
“The history of the sitar in jazz, that is the fusion of the sounds of Indian Classical music with Western jazz, dates back from the late-1950s or early-1960s when musicians trained in Indian Classical music such as Ravi Shankar started collaborating with jazz musicians such as Tony Scott and Bud Shank. Later jazz recordings containing sitar music include albums by Miles Davis, John Coltrane, Yusef Lateef, Joe Harriott (in collaboration with composer John Mayer), and Ornette Coleman.”
And so has the koto. From Wikipedia:
“June Kuramoto, of the jazz fusion group Hiroshima, was one of the first koto performers to popularize the koto in a non-traditional fusion style. Reiko Obata, founder of East West Jazz band, is the first to perform and record an album of jazz standards featuring koto. Obata also produced the first-ever English language koto instructional DVD “You Can Play Koto.”
David Bowie used a koto in the instrumental piece “Moss Garden” on his album “Heroes”. Paul Gilbert, a popular shred guitarist, recorded his wife, Emi playing the koto on his song “Koto Girl” from the album Alligator Farm. Visual Kei band Kagrra, are well known for using traditional Japanese musical instruments in many of their songs, an example being “Utakata” (うたかた), a song in which the koto has a prominent place. Jazz pianist Dave Brubeck composed “Koto Song” that, while not featuring the koto itself, is played to allow the piano to emulate its sound. Winston Tong, singer with Tuxedomoon, uses it on his 15-minute song, “The Hunger” from his debut solo album Theoretically Chinese.
Well-known solo performers outside of Japan include koto master and award-winning recording artist Elizabeth Falconer, who also studied for a decade at the esteemed Sawai Koto School in Tokyo, as well as koto master Linda Kako Caplan, Canadian Daishihan (Grandmaster) and a member of Fukuoka’s Chikushi Koto School for over two decades. David Horvitz pioneered the instrument into the contemporary indie rock scene playing on Xiu Xiu’s new album, The Air Force.”
Even the digeridoo and the glass Armonica have been used in jazz.
How successfully, I don’t know, but you could track down some of these recordings and see what you think.
Basically, if it makes noise, it can be used in jazz.