The world is abuzz with Twitter, Facebook and other Social Networking tools.  The numbers are staggering, 200 million users of Facebook alone - Facebook users would populate the 5th largest country.  While we are huge fans of social media and have helped numerous organizations leverage social media, there is one thing that we believe in to our core.  First you need to have an effective website.  Does it need to be fancy and have a memorable design? - not necessarily (unless you are in the web design business).  But it does need to authentically represent who you are and what you do.  Tweeting and Fan Pages are great to drive traffic, but if your website is a let-down, then potential customers will leave without completing a transaction (even if that means just gathering information about your organization and its purpose). 
First assess whether your web-site is effective.  Once you have accomplished that, by all means tweet to your heart's content.