Yes, it often can boost confidence. One of the things we can do with EMDR is use bi-lateral stimulation to reinforce experiences you've had with confidence, or even ones you can imagine. It can also reinforce experiences with or imagining other people believing in you, or qualities you want to cultivate in order to give you more confidence.
For example, I worked with a man who was afraid to speak in front of an audience. We figured out that he was afraid the audience wouldn't love him. When he realized this, we reinforced how much love he had in his life, and he realized he didn't need the audience to love him. He realized he was there to give out information he had, and they were there to receive it. He knew he had the information, so that wasn't hard or scary. When he felt stronger through the EMDR "resourcing" we did, he could hold onto how loved he was without anyone in the audience loving him. He realized at a deep level that he didn't need them to love him, and he wasn't scared anymore. He gave his presentation and felt totally confident.
Another example is a woman I worked with who had been molested as a child. She didn't have the confidence to stand up for herself as an adult. When we cleared the traumatic experience of being molested, and we reinforced her ability to stand up to the molester in her head, using EMDR, she developed the confidence to stand up to people as an adult.
Both resourcing--building people's emotional strengths--and trauma processing are part of EMDR's power. Both can be used to develop people's confidence.