According to my understanding, EMDR can be quick and successful when there is a concrete and isolated trauma, some particular traumatic event that stems out. I would be really surprised if it worked well with complex PTSD which by definitions is, well, complex and where it is really difficult to figure and recall what kind of incidents the trauma is really made up of. It could be that the whole childhood background was inherently traumatic, although it looked completely normal then because it was the only thing that the child knew.

I've had emotional backslashes that don't associate with really anything. No memory, no narrative, just a horrible intolerable feeling that comes from somewhere and then vanishes into somewhere, without me being able to make any sense of it. I doubt EMDR would be of much help here.