Apparently you should. I googled-wait for it-payroll and got several hits, including one payroll company with nearly 2,000 followers. Many of the followers are other types of companies and other payroll companies. Some might be customers or trade organizations. Many of the tweets are tips or information about services.
There are several things you need to consider when venturing into social media. One, is do you have the time or several people to maintain your effort? Don’t make it one person’s job, they might change jobs and then the social media account might languish. Another is will you have enough content? And maybe most importantly, have you set up guidelines for staff to follow? You want to be a-political, not over fanatical about sports or celebrities. You need to think about your page on twitter. Make sure your company name and logo are prominent; follow your branding. Make sure posted images are appropriate. Tweeting may not make much of an impact but it might be something to try if you have the resources. And lastly, if you find you don’t have relevant followers you can shut it down.