Question: Do wisdom teeth push other teeth and cause crowding of the anterior teeth? 

The simple answer to this is "no". There is no scientific evidence to support the fact that wisdom teeth cause late crowding and it is believed to be a natural phenomenon that occurs whether the wisdom teeth are present or not.

Removal of the wisdom teeth is unlikely to have any effect on crowded, crooked teeth. 
Many wisdom teeth can be simply removed under local anaesthetic. However some are complicated and need to be referred to a specialist .