HSS, although Type I diabetes does have a genetic component, it is not the standard of care to routinely screen children (or other first-degree relatives) of diabetics for the disease. Of course if one family member is diabetic, parents will probably be more likely to notice the typical symptoms (excessive drinking/ urination, weight loss) & will probably test the child’s blood sugar on their own if they are concerned.
Regarding Chevra Dor Yeshorim, it is my understanding that they screen only for fatal genetic diseases, but not for other Jewish diseases such as Gaucher’s.