Nope. Settling a bad debt does not remove it from your credit report. Only time does that. The fact you settled will be added to your credit report. Additionally, the difference between what you originally owed and the amount you settled for will be shown on your report as a "charge off". Items remain on your credit report anywhere from 5 to 10 years, depending on what it is. Generally, credit card debt is there for anywhere from 3-5 years and can be as long as 7 years depending on many factors. Things like a foreclosure will be there 7-10 years. Something like a vehicle repossession will be there 5-7 years.
But once you pay off or settle bad debt, as time passes it has less and less impact on your overall credit score. It helps things along if you keep your current debt, current and don't get behind on payments.