Somebody may come by with a different answer but with the right cable I don't see why not. Use the HDMI output on the Tv box and the proper DVI input on your monitor.
I beleive one can get those cables at places like Best Buy or Staples.
Most modern TVs and monitors are fairly interchangeable if they have HDMI inputs. A "tv" has a tuner that can receive over the air digital signals and always has some form of built in speakers. A monitor never has a tuner and may have speakers or may not have speakers. If the monitor does not have speakers how you output audio could be an issue.