The answer is yes, it can and has been done. There is a possibility that it could be completed in four years time. That would require a special curriculum to be designed that meets the approval of the American Board of Pediatrics for training in both areas. It will also require finding a hospital where the PICU and NICU don't mind sharing the cost of a combined fellow. Likely you would spend one year straight in each specialty. Then you would do your research, etc with various times on services in the areas. The more common pathway would be to finish training in one area and then to spend two years training in the other. Some of your research experience in the one would count towards the other.
I know all this because I looked into doing it and on some level am still considering it. It would give you the ability to basically run a children's hospital and I agree that it would be advantageous for some smaller community hospitals. The question I still have is could you really effectively practice both. The people I have heard that did this usually practiced one versus the other.