Depends on whose hands you leave it in, and how. If you let the Rim spin off to e.g. become the Liberated People’s Republic of Bredenia, you’ll get considerably more support than if you try to trade the territory to the Neo-Thaumatarchy for diplomatic favor.
The geographic scope of your influence as a prophet, advisor, eminence grise, etc. will be closely related to the scope of the faction you’re closest to (even if you’re not the one leading it) plus those who would count themselves as your allies. You’ll be involved in the decisions about geographic scope for the post-Hegemonic regime(s) you’re closest to, and can encourage them to think big or think small – and your priority there could of course be “what will help me spread my totally cool and awesome new cult” rather than “what will lead to the most stable long-term political order.” 
And yes, if you do want to lead a statelet, you’ll be able to have a wider sphere of influence, through factions allied or friendly to you elsewhere, or through particular paths of cross-border influence (economic, religious, koinon-ish).
While we’re talking about cheery post-Hegemonic scenarios, my world model is finally coughing out figures I’m happy to (tentatively) share around what happens, famine-wise, if Theurgy drops to zero post-rebellion – i.e. no blood used anywhere on the continent for harvest-boosting or grain transport, while the biggest noble estates that have been most intensively extra-harvested see a collapse in fertility levels. This version of the model assumes farmers shifting out of cash cropping everywhere to grow more staple crops and less flax, sugar, oil, and wine, but also some increase in land left fallow, because of social disruption.
Some headlines:
- The main area of Shayard in food deficit is the arid, urbanized lower Southriding (south of Vaulens) which would lack food for 4.7m people. Without Theurge-driven grain barges, Grand Shayard and Osterport would massively deurbanize as people move back into the parts of the realm that are still in surplus. The same would be happening in Shayard’s other big regional cities of Corlune, Rheges, and Veldrin, though those populations live much closer to districts that will still be in surplus. (The less-urbanized Rim is the only region of Shayard whose main city, Rimmersford, has remained modest-sized enough to feed itself by non-Theurgic means from its own hinterland.)
- Though there will be lots of social upheaval and hungry internally-displaced people, if you keep Shayard unified within its current borders, you’ll have enough of an agricultural surplus (even without Theurgy) to feed your whole population, plus enough of a surplus to feed about 15 million people elsewhere (after taking wastage in transit into account). Which will be nice to have, because…
- Around 7 million Wiends will be pouring out of Wiendwic and the great lowland cities of Alsztyn and Stezyc, looking for food. So would another 6m mixed Karagonds and Wiends from the two big cleruchies of eastern Wiendrj. (Those cities, Kiectos and Vrashtev, weren’t named on the last version of the core gameworld map, but to the northwest of Veldrin you can see their rich farmland–sadly not enough to sustain them in a post-Theurgic world.) So 13-14m people from Wiendrj on the move, all told, a disproportionate number of them with Phalangite training.
- Across Erezza, the only district still feeding its full population would be Rinocci in eastern Aveche (a small city in the middle of rich farm country). Elsewhere, 5.5 million people would be lacking food across the five most populous Erezziano districts (Soretto, Cocenza, Avezia, Sescia, Moncesano), with another million or so starving Phalangites and camp followers near the Halassur border (until they start rampaging somewhere in search of food). All told, the isthmus would be able to fully feed 12-13m fewer people than it has today. Not a strong position from which to hold the line against Halassur.
- In Nyryal, aside from a few small agricultural and military colony towns, every single district would be in deficit. The 4.4m horse nomads of the plains currently rely on grain trade with the cities and Erezza (via ports like Umri) for around 1/3 of their yearly diet; now all of their sources will be starving themselves. Nyrnakan alone will have 2m more people than it can feed. Overall, about 11-12m Nyr will be desperately looking for food.
- The nearly 900,000 Abhumans who currently depend on grain exports from the Hegemony wouldn’t be starving to death, but they’d be facing a massive shock to their livelihoods. Who knows what kind of political upheaval it might kick off in the Federation?
- I imagine most MCs will have Karagon a good ways down their priority list, if not at the bottom. But of course it will be the worst off, able to feed only 31% of a population that has grown to rely almost entirely on imported grain. Up to 26 million starving people will be pouring out of Karagon – most of them into Shayard, because that’s where the food is.
Now, this nightmare scenario might, in toto, actually be impossible. It’s incredibly unlikely that we’d see a Game 5 world where all these regions have to go for years without any form of Theurgic agriculture at all. Maybe if you manage to decapitate every other major faction in the game (or raise the wholesale anarchy level so high that they all collapse) but then fail to put any kind of new order in their place? Can’t say yet whether that’s going to be an achievable outcome or not. Kala/Kalt might be willing to go to bat for it in principle – a pathway that lets 50m people starve to death but prevents Theurges from reinstituting Harrowing (which currently takes over 3.5m lives a year) will “pay for itself” in less than a decade and a half, after all.
But much more likely is that we’ll see a mitigated version of the above famine, with a number of large post-Hegemonic territories (maybe including the MC’s?) where Theurgy continues to feed millions more people – whether because the ruling faction is a Theurge-ruled Harrower state, or has a non-lethal blood tax being used mostly for agriculture, or has self-fueled small-scale Theurgy being used by lots of new-minted magi for their own village’s benefit. It’s also possible that some other mitigating factors will crop up, like new super-seeds or newly researched agriculture techniques spread by certain factions to improve yields without heavy dependence on aether.
But we’ll definitely see lots of areas where the chaotic collapse of the Thaumatarchy leads to a partial or total breakdown in the Theurgy-fueled agriculture system – and thus to tens of millions of migrants, millions of whom will be starving. The scenario above should be taken as one extreme, but the challenges it describes won’t be entirely absent from anyone’s playthrough.