Is it possible to keep native edible self-seeding annuals under control?

I'm establishing a forest garden in northern New Mexico. Lamb's quarters (Chenopodium) and purslane (Portulaca) both grow here widely as volunteers. Has anyone purposely planted seeds in a section of their forest garden? Do they spread relentlessly? I read that purslane produces gazilions of seeds, and I've seen their tiny kind with my own eyes. Is this a bad idea? But GAWD they taste good. Same question with lamb's quarters. Their leaves are nice and mealy and full of Calcium. But... bad idea? Mike

At my place, lambsquarters and purslane pretty much only grow well in areas that I'm actively cultivating. They don't compete well with grasses, perennials, shrubs, or trees.

I have had no success so far in getting those two plants to infest my garden.  I would like to have both of them, but no luck.

I had trouble with purslane, so have it in a container now-it's good and healthy. Will try in the garden again once I chop/drop my winter veggies. Haven't tried lambsquarters yet. Good luck!

Yes I agree with Joseph that I don't think either of those likes other ground cover competition. I have a lawn of purslane coming up now in a annual veg area ie bare soil beneath/ between the primary crop plants. Perhaps this could be under a deciduous shrub though as they grow much earlier than anything else comes into leaf? mmm I shall give that a go and spread some seeding plants around under bushes.
Thanks!