I think you can probably do both. My regular therapist is also a level 2 EMDR practitioner, so I did both talk therapy and EMDR with him. It was useful to have one guy do both because sometimes something would come up during our talk therapy, and he would say, I can help you with that if we do EMDR, and I would agree, and next session we would do it. Very convenient. However, since not all therapists know how to do EMDR, I can see that your regular therapist might come across some issues that EMDR could help with and refer you out for EMDR work. But I would think you would still keep him/her as your primary T. I know sometimes people do similar with hypnotherapy. They have a regular T, but go to a hypnotherapist occasionally too.

Well, that was rambly! I guess I would suggest you ask your primary therapist this question.