No. To qualify for trade mark protection a domain name itself should function as a trade mark. Concretely this signifies that a domain name must not be used simply as an address to direct to a website, but to identify the products and/or services of the business, which provides products and/or services via the Internet. For example this will be the case of a domain name used in connection with a website that offers web-related services.
The registration of a domain name with an accredited registrar does not automatically signify that the same or similar sign will satisfy the requirements for trade mark registration. You can register as a domain name common or descriptive terms, that usually do not qualify for trade mark protection. Furthermore trade mark protection of a sign is needed only when such a sign will be used to identify and distinguish the commercial origin of the products and/or services of one company from those of another company.