In 1972, in Anti-Oedipus, Deleuze and Guattari make no mention, as far as I can recall, of smooth and striated space, or even of the nomad. (If there is it is hardly front and center).
Then, in 1974, Pierre Clastres publishes Society Against the State, wherein:
The space of nomad hunters [the Guayaki (or Ache) people of Paraguay that Clastres was studying] cannot have the same dividing lines as that of sedentary agriculturalists. The latter is structured into concentric circles, with a division between a cultural space comprised of the village and gardens, and a natural space occupied by the surrounding forest. In contrast, the Guayaki space is continually homogeneous, reduced to a pure extension in which the difference between nature and culture is seemingly done away with….
Then in 1980 in A Thousand Plateaus, we get the whole discussion of the nomad, smooth space, and striated space. I am only halfway through Clastres, but so far it seems pretty clear that he made a very big impression on D&G.