No, I advice you do not continue a relationship if you are not in love with him/her. It is not good for you and it unfair to your partner.
If you carry on with this relationship, you may end up frustrated because the relationship will become a burden to you. You might also end up cheating on your partner which will eventually cause a fight or breakup.
It is best you save yourself and your partner the stress, you should let your partner know exactly how you feel and you can both help each other to move on.
A relationship is a relation of truth. You may think that you can hide your feelings and continue the relation even when you do not love him or her. However, this can lead to fights, depression and even cheating later on. A far better and fair option for your Boyfriend or girlfriend is to tell them the truth.
Help them move on, rather than frustrating them with your loveless words. This is unfair for both you and them. Yes, they will be hurt in the start, but considering the turmoil they will go through in the future, it is kinder to do so.