Yes, school stress can cause illness. My child gets a stomach ache when he gets anxious - his description is that his stomach aches are similar to the "gforces that one feels in the tummy while on a roller coaster". We had a lot of these episodes in K, last year.
They vanished when we upped the intensity of afterschool activities, academics and enrichment. I suggest that you challenge your child not just academically, but also in other areas that would keep him involved - in our case, it was chess school, piano, martial arts and swim team - we did these pretty rigorously because my child has a lot of intensity and school just wasn't enough. We also used advanced curriculum to teach his favorite subjects.
My child started looking forward to school because he met his friends and socialized heavily there.
This year, we moved to an academics oriented private school and he is happier than before. We still afterschool.