asking leave for degree exam

It is quite difficult for you to get leave.  But try to apply for leave.  If you get leave it is OK.  Otherwise, take the examination later, when you are able to get the leave.  Training is equally important.  If you do not finish your training (it will not be given individually separately and one does not know when the next batch of training is going to be) it will affect your service.  Whereas the examination you can take later on also.  In your position, I will undergo training.  Try to sit for the examination later on.