Are you going to cover with cardboard and mulch and then leave it to clear the weeds, or try and grow in it? If you cut holes into it to plant through, perennial weeds will find their way out to the surface, so I would pick crops that can cope with that. I’ve planted squash and pumpkins like this to help clear a weedy plot and they do OK. I would say it will reduce couch grass, but not stop it. Bindweed loves it and gets stronger, but it is easier to dig out come autumn as it sends most of its runners through the mulch layer.
The manure in your picture is a bit fresh looking. I’d agree with Potterer that composting it for an autumn mulch might be a better bet.