If you can, then by all means do. That said, don't expect that the degree alone will speak for you. Writing is still an extremely competitive marketplace. You have to not only show why you're worth more, but also find the people who value quality over a bargain. It's not as easy as it might sound. I will also say that being a writer is about a lot more than getting the technical aspects down pat, and experience will polish your style, put you in tune with the marketplace, and get you used to the daily grind so you can meet deadlines without fail.
With all this in mind -- don't expect too much right out of the gate. There are a lot of degrees floating around out there, and a lot of clients who really only care if you can get the job done. Remember that the average content writer makes a lot less than published "market wages" for freelance writers who are affiliated with newspapers and magazines and what-not. Work on boosting your portfolio (these open-submission sites work great for that), get really good at pitching proposals, and don't be surprised if you have to take a few "just scraping by" jobs to get your foot in the door.