This question cannot really be answered with just a yes or no response, any one who answers it must be able to explain why because everyone has their own informed opinion on this question.
Some people would say yes because as all Christians believe, there is life after death with God, so there is no reason why we should wish to escape death but the main reason that most people would come up with for saying no is that nothing is as important as your own life and that you should protect it at all cost no matter what is required (there is a limit e.g. most people would not be willing to kill another person). Martyrdom is a strong reason, not so much in that “If I die I will be a martyr and everyone will praise me!” Which people who say no might accuse Martyrs of doing, and they would say it is wrong to do that, but more in the sense “Martyr’s were willing to die so should I be willing to show my devotion to God by sacrificing my life for others and to witness the truth.”
Some believe that when presented with death there are more important things than one’s self to think of, those being justice, mercy, forgiveness and peace while people saying no would counter with something like dying for your beliefs could be seen as suicide because you would just be letting yourself die and even God does not like people committing suicide. If you were in a place where Christians were persecuted and you died for your beliefs, you would be an inspiration for hope, so that your sacrifice may lead to better things for all people. This is a key point, that every sacrifice no matter how big or how small is important, but people in the same situation might not be willing to die because even Jesus the Son of God didn’t want to die, he prayed to God “my Father! All things are possible for you. Take this cup of suffering away from me. Yet not what I want, but what you want.” So people argue that there is nothing wrong with not being willing to die for one’s Christian belief.
In my opinion I would have to say that in most cases it is worth dying for one’s Christian principles e.g. if you were in a place where Christians were being persecuted and people were denouncing their Christian principles, then in order to show them that you should never give up hope and to inspire them, it would be worth openly showing your Christianity which would certainly lead to death. But in other cases it would be a waste, e.g. if you were involved in a project that involved helping others less fortunate than yourself and you were told that if you were a Christian you would be killed, then I would use one of the arguments put forward by someone who might have said yes as reason for saying no which is to put other things before one’s self by thinking about all the people that need your help so desperately.
In theory, there are more arguments as to why people should be willing to die for their Christian beliefs, but realistically even people who say yes, would in fact not be prepared to die, although there are some people who would, these are the true martyrs.