No. Trademark registration and domain name registration are entirely separate processes. A trademark does not automatically secure any domain name, and you must register the domain independently through a domain registrar.
What a trademark does give you is legal grounds to challenge a domain name that is identical or confusingly similar to your mark, where the domain is being used in connection with the same goods or services. The UDRP (Uniform Domain-Name Dispute-Resolution Policy), administered by WIPO, provides a mechanism for trademark holders to claim or cancel infringing domains without going to court.
For complete coverage, register both the domain and the trademark as early as possible. Neither automatically provides the other's protection.