Not sure how this translates to a composite material like MDF, but in the case of a wood to wood joint, the glue bonds as strong as the wood itself. Any screws or nails really only serve to align the joint and provide compression while the glue sets. Since MDF is fiberboard I'm sure its a bit different, but I'd think those reinforcing blocks you show on your website will add plenty of rigidity... much more than a handfull of screws I'd think.