As I said, the purslane in my organic garden is wild. I didn't plant it. I grow my veggie plants in raised beds and yet last year it was growing in between the lettuce plants and a few here and there but not a problem, as I added them to my salads and ate them. This year it's growing in with my tomato plants, my various lettuces, zucchini and other plants. This year it's a problem. But all I can do is pull them. Their roots are shallow so easy to pull.
My point is that planting them in with your perennials is fine but be prepared to have them migrate out of that area and perhaps into areas you won't be thrilled with.