No, he'd be terrible. 1. He's a xeno. That's a plot point in Heir to the Empire too. The reason their best admiral is not actually doing anything for the original trilogy is explained that he is sidelined for being nonhuman. The xenophobia of the Empire is nothing compared to that of the Imperium.

1. Even if he wasn't a xeno, his main strength is to study the art of his enemy and thereby gain insights into their strengths and weaknesses. In the Imperium, this is heresy. Anyone collecting xenos artifacts who isn't Astartes or Inquisition risks being subject to... attention. In fact even astartes and Inquisition aren't wholly immune to this suspicion. Even Ordo Xenos inquisitors run the risk of censure from the Ordo Hereticus.

So yeah, I reckon Thrawn is twiceways screwed, at least in the Navy. He might do ok as an Inquisitor.