The simple answer is no. You don't need a tree if you don't mind your cat scratching and clawing up other potentially valuable furniture and/or carpeting. Most cats develop routines where they have their favorite places and items to work their claws on. If you haven't provided your kitty with a scratching solution then you can't be mad at him or her for following its natural instincts to scratch and claw.
The best method is to offer your cat multiple areas to fulfill their scratching desires especially if you have more than one animal. Cats are actually very personable and like to be near their owners. You may notice some items in areas that are frequently occupied that your cat will continually return to for scratching. We have a couple larger cat towers in our main living room and a smaller condo with single pole and platform in our bedroom that our cats use regularly.
When picking out your cat tree or cat tower, one of the main differences between the cat trees is the scratching area. Some are covered with carpeting while others are wrapped with sisal rope. We used to have a couple with carpeting, but, after a bit of use the carpeting starts to either run and fray or tear away. You then end up with this post that has unattractive strings hanging off it. The sisal rope is much more durable than the carpeting for your cat to scratch on.
One other consideration might be the color you choose for your cat tree. For the most part the only two considerations will be to either match the cat tower to your decor or to your cat. If you choose the latter, your cat, you will spend less time cleaning because the hair that your cat sheds will blend in better with the fabric. You can also buy cat furniture to only match your home decor. This may cause you to clean your cats furniture more often due to unsightly hair.
To summarize, you should get your cat at least one scratching post, or cat tower as a solution to its scratching needs. There is nothing wrong with having more than one especially if you have more than one cat as I have found. The most durable and suitable scratching material I have found is the sisal rope wrapped furniture. If you match your tree color to your cat you will spend less time cleaning it.