Well, to an extent. You'd still expect that some neighboring state that *was* willing to automate more things would steamroller all the culturally-hobbled polities. Either the original sophonts, or their robotic successors, or some transsophont fusion of the two.
That's always the problem with the "It's the culture of the 3I" argument. Anything about 3I culture that creates a significant enough disadvantage for them would in the long turn lead to their destruction (or irrelevancy), because none of the neighbors are bound by that culture. You need to posit an exquisitely balanced set of interlocking cultural handicaps to have any hope at all of explaining the setting. And even then, somebody out beyond the nearest neighbors would sweep through and steamroller *everyone*.