Oh man, great question.

The answer is a complicated one -- but it's more or less inarguable that the vast majority of the Seleucid administration was Hellenic. When Alexander and his Companions rode in and took up the mantle of world empire, they didn't really reorganize the governmental apparatus of the various satrapies -- hence we have Seleucus, Antiochus and their successors playing the part of Babylonian "Kings of the Four Corners of the World", and the Ptolemies aping the Pharaohs of old. Politically, almost all important offices were filled by Greeks -- there are exceptions, however. [Bagadates I] (http://en.wikipedia.org/wiki/Bagadates) is an excellent example -- he's precisely the type of man you're asking about. He seems to have been a sort of vassal priest-king, and the religious nature of his office is, I think, quite significant. In matters of traditional Iranian (and Babylonian, and Egyptian) religious ceremonies, native officials tended to be left in charge -- the Macedonian conquerors tended to enjoy playing Zeus more than Ahura Mazda or Marduk. But, the presence of a man such as Bagadates of Persia does show that non-Greeks could certainly attain high office. It's probably equally significant that Bagadates and his descendants broke free of Seleucid control literally as soon as they could, in the wake of Magnesia in 190 BCE. He and his dynasty may have grown out of an earlier precedent: in the Wars of the Successors, there are occasional references to Persian civilian administrators being paired with Macedonian military commanders to govern satrapies as well.

In short, in Persia, as in Babylon, Egypt, Bactria, and all the regions of the former Persian Empire, native aristocracies maintained great influence, even if they were occasionally snubbed by the new transplant gymnasia -- and that influence could and did lead to separatist tendencies from the greater Seleucid administration.

Hope this was helpful!

Source: Peter Green's incomparable work on Hellenistic history, Alexander to Actium.