Undersowing with green manure seeds

I've just heard a suggestion that once vegetable seedlings take hold, stop weeding around them and allow the weeds to grow - this prevents the soil drying out and the veggies need far less water and far fewer bugs.
Then I searched the idea of undersowing with green manure seeds. Has anyone tried this?

I'm willing to buy a couple of packets of seeds to give it a go, but would also like to know if I can collect my own seed from this.