Yes, you certainly can use a fitted sheet to cover your couch. This is a great option for people on a budget, but fitted sheets do not offer the best protection. Sure, they will keep hair and dirt off of your couch, but odors can easily pass through the thin fabric.
What’s more, fitted sheets can be easily snagged by a dog’s claws. You also might be put off by the look of a large sheet slumped over your couch. Chances are that your sheet is going to be ill-fitting and wrinkled over your once-lovely couch.