My 2cents. Since the height of that rack where the cross support is, the bed can still come out of square with a bit of load or impact.
For example, if the cross bars were down at the attachment point, right at top of bed rails, it would protect it more but still not 100% as the bottom is still unprotected and can collapse with a harder impact or uneven load.
Bed stiffeners are important for the structural support of the sides at the most critical area, the bottom.
Will that rack help, yes. Will you ever actually need bed stiffeners? Maybe. Just be smart about the load on the rack.