Speaking with my OT hat on:
issues related to balance, fine motor skills and organization skills sounds like the OT is actually addressing a sensory integration disorder, more recently also termed sensory processing disorder. Sensory integration is a neurological process that involves our brains acquiring sensory information, combining it and processing it (integration)and then being able to respond to the information. Sort of an "input, process, output" model of neurological function. A good book is SI and the Child, by A. Jean Ayres, PhD.
Most children on the autism spectrum, including kids with Aspergers, display some degree of SI dysfunction. BUT....the presence of SI dysfunction DOES NOT mean a child has autism. Many children with SI dysfunction have other concurring diagnoses or NO OTHER diagnosis.
To answer your question, yes, children who have balance and fine motor problems can also display problems with organization skills. The connection is typically based in the spatial/temporal skills, perceptual and higher level cognitive development that are disrupted because of lower level physical skill development.
