I'm reaching a point in my food-forest where nothing receives tender loving care but I'm also hitting that tipping point where nature takes over.
Last year I dug a large ditch just beyond the white peonies in the photo below and filled with a bunch of wood and debris. I then scattered wildflower seeds like yarrow and planted a few sunchokes.
I started Martha Washington Asparagus from seed and planted out a bunch of tiny seedlings in the freshly dug area. A bunch of them didn't make it (or I can't see them) but a bunch of them did. There are probably some hidden I don't see. I will go out and clear some of this up this weekend.
The asparagus plant that is the most vibrant was planted next to a baby Japanese maple that volunteered, and I re-planted. I also broadcast some clover and let it run. The plant you see in the picture has been trimmed quite a bit because it started choking out the maple.
In the large patch, I planted alpine strawberries next to the asparagus but Alpines are a slow grower.
If you use strawberries I would go for a full-sized everbearing variety.
My asparagus seedlings are being grown like they are wild. They are making it. With a little hand weeding, they would explode. I'm always nervous to keep things too neat with baby plantings because the wildflowers provide, shade, moisture, and refocus pests.
Don't do what I did and use mint and sunchokes. Yeah, I should have known. So to answer your question, my asparagus is growing with alpine strawberries, wildflowers, weeds, Japanese maple, and clover and they are making it. I think most ground covers would work.