The simple answer to your question is "not necessarily".
Several studies have looked at the natural history of wheezing and asthma in the first six years of life. In one study, 60% of children with wheezing in the first 3 of life had no wheezing at 6 years of age.
This study, and others, support the idea that there are at least two groups of children who have wheeze and asthma-like symptoms at an early age. One group tends to have intermittent symptoms at an early age, usually in relation to viral illnesses, and go on to outgrow the symptoms as the children get older. The other group, which tends to have later-onset and more persistent symptoms, is characterized by allergies and a family history of asthma, and is at an increased risk for asthma later in life.
It has also been estimated that between 30% to 70% of children who develop asthma are markedly improved or without symptoms by early adulthood. This is contrasted with the fact that wheezing and asthma in adolescence is associated with a high rate of persistence into adulthood; however progressive worsening over time is unusual).
Basically what I am trying to illustrate is that there is a significant proportion of people who are diagnosed with asthma and later go on to improve, many without any symptoms at all. The chance of this happening increases if you are diagnosed as a child.
Reference: Litonjua AA, Weiss ST. Natural History of Asthma, Literature review. UpToDate online 18.2, May 2010.