Short answer: No.
Cats are obligate carnivores. Note the "obligate". While they can process and obtain nutrition from some vegetable/plant matter, they cannot receive or produce all the nutrients they need this way.
Omnivores (like humans and dogs and many others) have certain metabolic pathways available to them that mean that they can make use of both plant and animal matter fairly well. We need vitamin A. We can get this directly from other animals (meat), but our bodies can also manufacture it from beta-carotene which is found in many plants. Cats cannot do this. Vitamin A does not occur in plants, only vitamin A precursors, which cats cannot adequately make use of.
Same story with taurine, vitamin D, and many others.
Cats have a carnivore's digestive tract and a carnivore's metabolic system. With very careful balancing and supplementation, it might be possible for a cat to survive on a vegetarian diet. However, there is a difference between surviving and thriving. Cats should not be forced to eat a vegetarian diet.
If your friends wish to maintain a vegetarian/vegan household, that's fine, but they should look into pets who are suited for such a diet in that case. Cats, unfortunately, are not one of them.