I know of a child who had it and it was successful. I also know two adults (early 20s) who went through trauma as children who had it. For one adult, their trauma was a single big event and EMDR worked well.
For the other adult, it broke down as a therapist and had to be stopped. That adult had suffered long term repeated trauma and has an ongoing mental illness as a consequence. For them, the reliving of the abuse was too much and they have been referred for intensive therapy at a specialist centre that starts with learning coping mechanisms in a group and goes on to individual therapy for a year minimum.
This therapy break down may have been down to the EMDR therapist, who was not inexperienced but was also not highly experienced, so may not have been the best person to treat someone with a complex traumatic history. Although the therapist did the right thing when he explained he could not continue the therapy, the impression the adult got was one of their emotions being something the therapist could not cope with - which would have contributed to the break down of the treatment.
As other posters have said, it can be highly effective, but I would say that if possible it's best to really look at how much support you/your child might need when working through such difficult memories and to question that therapist on how much experience they have of what you might be working through. It can be a really tough thing to do when first meeting a therapist, but can be better than beginning therapy and having to stop. It can also be worth, if you/your child hasn't done a therapy where you learn coping mechanisms, looking into that first. Sometimes, learning DBT techniques or similar can be very helpful first, and finding what works to self-soothe. Lying under or wrapping up in a weighted blanket, focuses on senses by doing something sensual, practising mindfulness (in age appropriate way), rocking/going on a swing, bouncing on a trampoline or trampet and (age appropriate) thought challenging techniques, and lots more, can all be really helpful at getting through the time in between the therapy when you/your child is coping with those memories brought up during the EMDR therapies. EMDR does cover some techniques like this itself, but learning and getting used to practising them prior to beginning therapy can really help it to succeed.