Abstinence until a certain age of maturity is reached is probably a very good idea but it is not going to be a workable one for many young people. So, while it may work, so does education about birth control as well as the other forms of sexuality that can be explored.
Yes, abstinence works to decrease teen and single mother births, because it gives girls and women reasons to not have sex. If people think that they will not be criticized for not having sex, and that they are doing the "cool" thing by waiting, they will not feel like they have to conform to peer pressure. Abstinence gives young women a choice among behaviors.
If students and teens are using abstinence than it would obviously decrease teen mothers and single mother births. Keeping yourself from doing mature acts at young ages assures the teen will have a better future and be able to move towards a better life and learn and get an education.
Studies have show that if you teach abstinence but not safe sex, it does not decrease teen pregnancies. Teenagers will still have sex, even if a teacher tells them not to. If you insist on teaching abstinence, you must teach safe sex top-level that way the teens who do have sex will know how to prevent pregnancies.
Abstinence-only education has been proven not to be effective repeatedly throughout the world, so its confusing to me that people continue to ask this question. I will repeat: abstinence education does not work. Attempting to make a rule dictating the private lives of teenagers by telling them to not do something they really (naturally) want to do is almost comically absurd.
If abstinence was actually carried through with, yes, obviously it would decrease teen and single mother births, no intercourse no pregnancy. But, what abstinence does in the real world where people have hormones is it makes them refrain from sex for a while until everything builds up and the person has to get with somebody. So, in the long run, no, in reality it changes little.