I've got the variegated bishops weed encroaching from a neighbor. In all the years, I've never seen it bloom. It probably would if I weren't constantly digging it and pulling it and scuffle hoeing it to keep the infestation at bay. From the images on google, I don't think the flowers are worth a tinker's damn anyway.

It will not confine itself to being a "border" plant.

Bishops Weed, aka Gout Weed, Snow on the Mountain, and some other less desirable names, does have a somewhat inconspicuous white flower. This quite invasive plant is often sold as a fast growing ground cover and more for the foliage then the flower.