No, URL ownership and trademark protection are two parallel but very different systems. Owning and using a URL is not enough to protect your name as a trademark, other than providing some Common Law rights through use.
In fact, many founders register or buy a URL and start building their brand around it, only to find out, too late -- after they get sued or receive a cease-and-desist letter -- that they can’t use that name for their planned business, because someone else has prior trademark rights.
It is unwise to spend a lot of (or any) money buying a URL, until you’re sure you can actually use that name as a trademark. (This is just as true, whether you plan to actually register your name as a trademark, or not.)
Before buying a URL, try and get some confidence in your potential to use it for your planned goods or services. Our automated search service here at www.namingmatters.com rates trademark risk; combine that with some internet searching of your name and goods to check for Common Law use.