Well, today is another double sprouts day, so here's an update with my 2 cities:
Elven city, all quests complete, 3rd grand prize unlocked, 80 nuts left.
Human city, all quests complete, 745/800 on the 3rd grand prize, 9 nuts left.
So it is NOT guaranteed completely, though I still have about two weeks of daily quests and nut foraging to make up those missing sprouts. I did gamble a few times on the sawmill for both cities, but maybe 3-4 rolls for each.
So you can go for the 3 grand prizes, but you sacrifice your chance to get most everything else. On the other hand, you come away with TONS of instants. I am utterly buried in them and must resist the urge to make every upgrade instant so I don't become reliant on them.