Tradescantia chrysophylla, also commonly known as Baby Bunny Bellies, is an easy care houseplant with fuzzy foliage! This plant is perfectly named, it really does feel silky just like a baby bunnies belly! It's a climbing or trailing plant and will thrive indoors with sufficient lighting.
In short, the answer is a resounding YES. The plant has sap within the stems that will bother your cat's digestive tract. It's important to note that usually there isn't a toxic reaction to consuming the leaves. But there's also no reason to risk it, when part of the plant is definitely toxic.