The short answer to this question is no. For many years there was a misconception that as the wisdom teeth started coming in they would push the other teeth forward causing them to become crooked.
Now with more research from the orthodontic community we now know that wisdom teeth cannot exert enough force to move other teeth. When teeth become crooked again after orthodontic treatment the most common culprit is not wearing your retainer. The bone surrounding our teeth is a living tissue that is constantly changing over throughout our lifetime. Because of that turnover of bone the teeth can shift as we grow older.
To prevent any major shifting of the teeth it is important to wear retainers for life.
So then why do wisdom teeth have to be removed?
Not all wisdom teeth need to be removed. However, most people do not have room in their mouth for their wisdom teeth to come in properly. When wisdom teeth only partially come in they can create a path for bacteria to get down under the gums to the other part of the tooth and cause cavities, gum inflammation, or other problems.
Some impacted wisdom teeth can cause other issues such as cysts or damage to other teeth. To prevent any of those problems from occurring your dentist may recommend having them removed.
Many people will have wisdom teeth removed when they are younger before any of those issues arise so that they do not need to worry about them happening in the future. If your dentist recommends to have your wisdom teeth removed, rest assured that it is a very common procedure that is usually fairly straightforward.