You don't get instant Twitter traffic from a huge follower count unless you are a somebody and people actually read your tweets. In the short run, you get traffic from Twitter with retweets. In the long run, tweets containing your urls will help you rank your site in the SERPs.
Going on twitter and adding a ton of people (who you hope will add you back) is an idiotic strategy. You will have all of these people shitting up your stream, so you probably won't read anything they are saying. They don't read their stream, and you don't read your stream, so who exactly are you knuckleheads actually talking to?
If you don't read the people you are following, you can't build relationships. No relationships, no one is reading you, clicking links, or retweeting.
Twitter marketing takes time and work. You can't treat it like spammy fire and forget link building project if you want to get a real benefit from it. You have to put in time, work and dedication.