Answer: yes it can.
Having just got Mayflower, the new love of our indoor life, and living on the 5th floor, we were wondering if we can open our screens or not. Mayflower loves to sit on the windowsill before the screen and we had contemplated opening the screen for her so she could go out on the ledge, closer to the “real world” outside. (Poor cats! Have to stay all cooped up in this artificial atmosphere! If only they could go climb trees! They are kind of like the bubble boy in this respect, non?)
So I did some web research, and apparently this is a common question with a ready answer. So many injured cats come into the vet’s office with broken pelvises that there is even a term for it: Feline high-rise syndrome. Since tons of people own cats in high-rise apartments, like us, and many of them leave their windows open, some of those cats fall.
Cats won’t under normal circumstances, because they have amazing depth perception, body control, and agility. So they can comfortably wander on your window ledge at the 15th floor, or walk on the skinny connector from one ledge to the next. But if startled, scared, or provoked (by the urge to catch a bird!), the worst can happen. If the cat were in a tree, where it evolved, it would still be able to right itself (test show it can get its feet under it within 20-odd inches) and latch onto a branch (or even fan its body out, as it does for free-fall, in a flying-squirrel effect). But from the ledge it is helpless in this unnatural environment, where there is only space below it. If someone drops a plate, if there is a bird lands on the next windowsill, or if the cat goes to sleep on the ledge, it can fall off. The evidence plentiful of cats that have fallen. Usually they don’t, but sometimes they do.
Here are a few links:
High-rise syndome #1 here
High-rise syndrome #2 here
Video story of a cat that fell 26 stories and survived
A pet-veranda/cage so the cat can safely go out into its 2-foot treehouse/cage to contemplate the world.