Fun question, and the answer is genuinely interesting because fluffies were more or less designed as a walking invasive-species thought experiment.
The case for yes: The canon gives them r-strategist stats that would make a rabbit blush — gestation measured in weeks, litters of several, sexual maturity almost immediately, and an indiscriminate appetite for grass and basically any crop. If you take "doubles every three weeks" at face value, a founding population of a thousand hits the billions inside of eighteen months. And there's real precedent for the underlying mechanism: rabbits in Australia peaked around 600 million and did serious, lasting damage to pasture and topsoil, and desert locust swarms have pushed whole regions in the Horn of Africa into food emergencies. Small herbivore plus exponential growth plus no predators is a legitimately scary combination.
The case for no: everything else about them. Exponential curves only matter if the organism can actually cash them in, and fluffies are canonically among the least survivable creatures ever imagined — they freeze at the first frost, they're too stupid to forage well or flee, they have no defenses, and they die of what the lore treats as sheer emotional distress. Very high fecundity paired with near-zero survivorship is just a population that churns, not one that conquers.
Geography seals it. A huge share of the world's calories comes from temperate grain belts — the Canadian prairies, the Russian steppe, the northern US, northern China — all of which have winters that would wipe out a fluffy population annually. They can't fly, can't swim, and can't cross an ocean, which is exactly why locusts can threaten a region and rabbits couldn't threaten a planet. And unlike an insect swarm, a fluffy is slow, conspicuous, and trivially killable, which is the entire premise of most of the fiction written about them.
Verdict: within their own setting, a regional agricultural crisis in a warm temperate zone is very plausible — think Australian rabbit plague, with commodity price spikes and localized shortages downstream. A true global food shortage is unlikely; they'd be an expensive nuisance that gets contained in the places that matter most for calories.
In our actual world, of course, the probability is zero, since the only thing fluffies have ever successfully consumed is bandwidth.
