The short answer is “NO, not at all”. The long answer is “Maybe”.
Promoting your website, service or products using Twitter is very similar to using email marketing to get the word out. You use social media networks to connect, interact, respond to and push out information about yourself and your business. Social Networks, like Twitter, offer a way for you to stay connected to your client/customer base and provide feedback, offer advice or incentives and handle complaints or questions.
Since Twitter is a nofollow site it is not good for building back links and getting pages indexed in Google. However, if you post updates via Twitter you may be able to help your website in rankings if you place your updates on your site. The more relevant, focused content you have on your site the more authoritative your site will be regard as to Google.
Lastly, many indexing services exist out there that will take Twitter posts and host them on their sites. These sites may get indexed in Google and so you can still get some of your Twitter posts indexed by Google in a very indirect but valuable way.
If Twitter is not currently part of your marketing strategy it should be. The benefits are substantial from a marketing standpoint and it just may help you, in the long run, rank a little better in search engines. Good luck