No, during EMDR therapy you are simply guided into a relaxed, almost meditative state where you are fully aware of your surroundings and are completely present the entire time. In fact, being fully present is a necessary part of how working through your past occurs, while also not retraumatizing you as you connect with the memory networks of difficult past experiences.
We are essentially helping you put one foot in the past experience while keeping the other in the present, working to connect the two so that the knowledge of your current status ("I got through it," "There's nothing wrong with me," "It wasn't my fault," and so forth) can positively impact the past negative experience we're helping you connect to, literally merging these two memory networks in a healthy way.
This dual awareness couldn't occur if you were put into some hypnotized or trance-like state. Instead, we are just starting sessions by helping you relax and notice your present experience (body sensations, emotions, and thoughts) so that you can incorporate your body and emotions into the process.