Various technological applications for body posture correction have been proposed in order to improve handwriting or facilitate its learning for children, under the assumption that a better posture promotes better handwriting. However, very little research investigates the correlation between body posture quality and handwriting quality. Moreover, investigating this correlation typically necessitates the expertise of human observers, leading to high costs, slow progress, and potential subjectivity issues. Consequently, this method may not be suitable for educational environments that require prompt feedback and interventions. In this paper, we present a fully-automated pipeline for the real-time assessment of body posture quality, which builds upon validated scales from ergonomics, which relies on red green blue depth (RGB-D) camera data to compute the rapid entire body assessment (REBA)/ rapid upper limb assessment (RULA) body posture scores. Together with a state-of-the-art tool for the automated, real-time assessment of handwriting quality, we applied our pipeline in an experiment at school involving 31 children, to quantitatively and objectively investigate (i) the correlation between body posture quality scores and handwriting quality measures, as well as (ii) the impact that interventions aimed at improving the children's body posture have on their handwriting quality. Our findings (i) demonstrate the correlations between specific postural element quality assessment scores (e.g., neck score) and handwriting dimensions (e.g., static features), and (ii) indicate that interventions aiming to improve body posture quality also have an immediate, significant positive effect on handwriting quality.