Of course, it can, and there are likely to be thousands of websites on the internet whose sole purpose is to promote and sell affiliate products.
If you were just starting out and were looking for a way of making money online, this kind of website could be a great first business. By selling other people’s products you wouldn’t have to deal with suppliers or customer service problems as the product owner would be responsible for them. You would receive a commission for every sale you made, and you have an almost unlimited choice as to the types of products or services you might want to promote,
If you already have a business, your website design could incorporate the ability to promote affiliate products. These would obviously need to be related to your own business, and certainly not compete with it either. It would seem strange to visitors if the affiliate products you were promoting were the same as what your own business sells.