Yes. They feel pain, they feel hurt, and they feel betrayal (about many things). They experience a range of emotions. Feeling emotions is not the problem and probably not why you are asking this question. The problem is while they feel pain for themselves, they lack empathy for others. So, even if they hurt you, it’s unlikely they can feel your pain but instead focus on why they were hurt in the situation. Often, avoiding any accountability for their behaviors. This is part of the disorder.
Love to a narcissist is not what we would view as true love. Their love is purely about giving them fuel. It’s conditional and self-serving only. Instead of “I love how good of a person you are”, they may be thinking “I love how good of a person you are to me and that you keep giving no matter what I do to you.” It’s only about them in a relationship, not the two of you.