Not the first time I've done this, it works a treat. It's not as fast as just using a rotary hoe and then planting but it's worth it for the reduction in weeds
Discussion
Does the cardboard break down, or did you mean the grass breaks down underneath the cardboard? I usually let it dry and set it on fire. I don't know what's better.
They both break down together to enrich the soil, the cardboard stops the grass from growing back up through the new garden bed and taking over again. It's one of those varieties that just keeps coming back if you don't cover it.