Yes it will keep cats out if you zip the zipper, tighten the drawstring and tuck the bottom under the crib/playpen or anything heavy. However this is not designed specially for cats.
It looks the best for cribs with flat tops. But will be functional on convertible cribs if the height of the net (43'') is enough to cover your crib.
The playpen net (41 by 28 inches) should fit a mini crib
Watch the video demonstration here https://youtu.be/od8yIF_yO7I