This isn’t a simple yes/no answer. First, you didn’t mention a specific product, and they act differently.
Wired cams (Floodlight Cam, Spotlight Wired, Spotlight Mount, Stick Up Wired) use video analysis for motion detection. If the cats enter the zones you draw, it’s likely that it will alert, even on low settings, unless the cats are far away. Wired cams have a 5 position slider which regulates what percentage of the frame must change for an alert. If the cat is far away, it may not trigger on the first or second setting. But if the cat is really close, which makes it appear larger in the frame, it will likely set off at any level.
Battery cameras (Spotlight Battery, Spotlight Solar*, Stick Up Battery) use passive infrared (PIR) motion detection that relies on heat. This makes it a lot more likely that cats will set off the motion at any sensitivity level, and you can’t draw specific zones. You’ve got three sensors, left, center, and right, and you can turn them on or off individually, and sensitivity is somewhat adjustable. As an example, if it’s cold out, the cats will give off more heat compared to the surroundings, and more likely to trigger motion alerts. But if it’s 100F out, they probably won’t, but even people may not at 100F, since it’s so close to body temp.
So to summarize, depending on the camera, and where it’s aimed and where the cats get to, it may or may not. But the odds are good that with 7 cats back there, you’ll get at least some false alerts with either wired or battery cameras. There’s really no way to say for sure without trying it out.
*Yes, the solar version is still a battery camera, it just has a solar charger. So it will operate like a battery cam whether the solar is connected or not.