Yes - cats a mesopredators. They hunt at random anything they can. In nature, mesopredators are usually suppressed by apex predators...

Did not know this, thanks.

No - feral cats numbers are exponentially high and on the increase.

Yeh, but in my hypothetical there are no feral cats. I appreciate that's not reality.

... wildlife that has not evolved to be wary of cats.

But in my hypothetical, we'd be talking a cat-to-bird/rodent ratio of like 1:10 000, minimum. I don't see how that cat knocking off 2-3 per day (at most) of those birds/rodents can be a problem for that ecosystem; it seems within the bounds of sustainable acceptable losses (please correct me if wrong). Only exception might be very specific endangered species with tiny and delicate populations.