Ah, 'kay, didn't know

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Does despotism exclude a working bureaucracy?
Well, it's not really a question of despotism. As Cutlass indicated (although I wouldn't have put it in that sense), nobody can rule entirely by fiat. Even an autocrat has to rely on the people who work for him to carry out his decisions. There are information gaps and lags, and questions of interpretation and judgment in implementing given orders. People don't, as a rule, just follow orders "because"; they tend to need some sort of inducement to do so, whatever it is.
And in the relevant period, "autocracy" was even less of a Thing than it might've been at any other point in history. Much of the last few decades of scholarship has been devoted to demonstrating the importance of consent and consensus to various forms of government at various levels. For example, Louis XIV famously established an "absolute monarchy", supposedly cutting the nobility out of government and relying on a new bureaucracy of intendant servitors. Yet in reality, Louis spent a great deal of time co-opting and cajoling the aristocracy into supporting him, and staffed most of his higher military and civil positions with aristocrats from various factions and allegiances. His intendants were not simply blind obedient servants, bending to his will, but ended up exercising a wide latitude of interpretation in what they did, and their footprint in French local government was in fact remarkably small.
Broadly speaking (a point which cannot be emphasized enough), the fiscal-military state was a phenomenon of the early modern era, in which success in war was, it is argued, closely related to success in securing funds. Those funds were secured through a wide variety of means, but many scholars have emphasized that ostensibly "democratic" - or at least more overtly consensus-based - systems tended to be better, over the long run, at getting money. Legislative assemblies, for instance, often made borrowing easier; they helped increase confidence that the state would not embark on imprudent fiscal policy, thereby wasting a lender's investment, and were themselves often closely connected to key financial institutions and leaders.
Over the long term, too, it's not clear that non-autocratic systems were any worse at making good and timely decisions than other ones. For one thing, again, there was no such thing as an autocracy. Most kings and princes had to secure the consent of key figures in their governments before they could embark on a given policy course; this was easier for some than others, of course, but the point is that consensus-building was still involved. On the other end of the scale, most "democratic" systems, e.g. the Dutch Republic or the English-British monarchy, were quite capable of investing extraordinary decision-making powers in individuals or bureaucracies devoted to the task, thereby divorcing such decisions from assembly politics to a degree.
The first wave of fiscal-military scholarship in fact
focused on the Dutch and English-British experiences of early modern warfare, and sought to answer the question of why those two states did so well, relatively speaking, despite the apparent problems a country ruled by an assembly might have. Now, the extent of their success tended to be exaggerated, and now many scholars are looking at the warmaking institutions of other states, e.g. the Habsburg monarchy, and pointing out similarities and even advantages that those states enjoyed. But the overall conclusion - that "despotism" and "absolutism" are not really relevant categories in early modern history and have relatively little to do with military or political success - remains unassailable.