Yes, they can. A customer is: A person or organization that buys goods or services from a store or other business. A consumer is: 1.A person who purchases goods and services for personal use. or 2.A person or thing that eats or uses something.
So you can see from the definitions that the two are not mutually exclusive. I can think of lots of types of businesses which could serve both customers and consumers. If someone doesn't know the real answer to a question, they shouldn't try to answer. It is better to remain silent and be thought a fool than to speak and remove all doubt.
A company cannot have both customer and consumer at the same time. The consumers being the final users of the product, a company needs to sell its products outside the company and not inside. It would be profitable if the customer comes from outside, rather than within the same company.