For my DD the connection came because her articulation problems WERE affecting her writing. And her use of AT.
Voice recognition software was having trouble understanding her and she was writing/typing words as she pronounces them. She routinely mixes up "R" and "W", hard "TH" and "D", soft "TH" and "S", etc. Her college level vocabulary was tested only as "high average" by the literacy specialist because of things like reading "eager" as "eagle". She has been identified with just about every possible LD so her situation is more complex but it points to the need for a thorough evaluation.
If I understand correctly you now have a private psych report that should qualify him for a 504 to address dysgraphia and in school SLP saying he can qualify for an IEP for speech. This tells me you don't have the complete picture yet. As DeeDee said a full evaluation and an AT eval are probably a good idea. He is still little - the full extent of his difficulties may appear gradually. I think it's a good idea to get out in front of it.
