The answer to this question depends somewhat on what your definitions are of conversion and Christian. If you mean does one have to change their life to be a Christian, then the answer is definitely yes. Some of the definitions of conversion from dictionary.com seem to parallel a definition of repentance. Some of the definitions are.
The act or process of converting; state of being converted, change in character, form, or function, spiritual change from sinfulness to righteousness, a change of attitude, emotion, or viewpoint from one of indifference, disbelief, or antagonism to one of acceptance, faith, or enthusiastic support, esp. such a change in a person’s religion. In other words, your mind is being converted from thinking your action are OK to repenting of the wrong you have done. A Biblical definition of Christian is someone who is Christ like.
The Bible teaches that one must repent in order to be saved. Luke 13:3 states, “Unless you repent, you too will also perish.” This verse in and of itself should be enough evidence that at least inwardly a person must convert in order to be saved. Jesus himself preached, “Repent for the kingdom of heaven is near.” In Mark 1:15 we are admonished, “Repent and believe the good news.” In Mark 6:12 it says, “And they went out and preached that people should repent.”
Repentance means that you are sorry for what you have done. It means that your mind has been converted from thinking that what you did was alright, to knowing that what you did was wrong. This is not possible without a conversion experience. However, it is not necessary for a person to walk down a church aisle and make a public confession in order to be saved and thus become a Christian.
In 2 Corinthians 5:17 the Apostle Paul told the Corinthian church that we are a new creation in Christ. This would seem to meet the definition of conversion from dictionary.com where it says, “Change in character, form, or function, spiritual change from sinfulness to righteousness.” A Christian does not always become a totally different person right away. Some people are saved out of a life of dire sinfulness. These people will usually take some time to break old habits and have a totally new life. Though their life may not completely change right away, if they are truly saved, their attitude will change immediately.
So the answer to the question is yes. It is necessary for a Christian to have a conversion experience. Someone who has never had a conversion experience is not truly a Christian in the Biblical sense of the word. One cannot be a Christian unless they are a new creature as the Apostle Paul wrote. Christ derided the Pharisees for having only an outward appearance of holiness and no change of heart. He called them whitewashed tombs which hid men’s bones while appearing nice on the outside. It is necessary to have a conversion experience to be a true Christian.