That's a difficult, and a good, question. Emotions are a part of the human experience and they have a place in debates and discussions. Effective speakers routinely inject emotion into their presentations. In a manner of speaking; it is passion, or emotion, that instills the drive to share an opinion with others. Apathy makes for a very poor and boring debate. On the other hand, emotions can sometimes overshadow reason.
As others have pointed out, the use of emotion also carries a risk. An excessive, or inappropriate, use of emotion can alienate listeners and diminish the argument. Intent is also important as one other person pointed out. If used in an attempt to deceive, destroy, or degrade the motive can overshadow the argument. In my opinion, the most important factor is whether the emotions are real; people can usually tell the difference.
I think it's wrong for us to believe that we as humans can live absent of emotions. That simply isn't possible. Emotions are at the very core of our personal judgments and they give a lot of value to the experience of life. Emotions play an important part in debates and in arguments. However, this does not mean that emotions should be used against the implementation fairness and justice. At their heart justice and fairness acknowledge the role that every individual's needs and concerns play in society, many of which are grounded in crucial emotional foundations. To oppose fairness and justice is therefore to oppose emotional equality/ fairness throughout society.
Emotion is useful to add emphasis to points. As long as it does not interfere with your reasoning, such emphasis can be potent in ensuring an audience understands the main points of your presentation. Where most people go wrong is when they replace reason with emotion...That will simply add emphasis to the lack of reasoning in your argument.
I don't think it's justifiable to use emotions to sway an argument because it's a form of negative manipulation. Arguments should be made with logic and facts, rather than with emotion, because if an argument is only made with emotion, then provoking an emotion is a form of attack on whoever is on the other side of the argument.
When you use emotions with no rational reasoning to sway people to your side of an argument its dishonest and you should be ready to defend yourself or get criticized by people that realize this tactic. If you are using a testimony that backs the facts then its acceptable, but you have to realize that many people will not consider this as fact and it could hurt your argument.