Coprosmas are so innately undemanding and complaisant to all sorts of conditions, that some types self sow and thrive untended in riparian or coastal environments. If they were more aggressive, they would likely naturalize (proliferate as if native) where the soil does not get too dry through summer. With such glossy foliage that looks like plastic, they might be appealing weeds.
Coprosma X kirkii is a resilient ground cover that mostly stays less than two feet deep and five feet wide, although overgrown plants can get three feet deep. Varieties with colorful or variegated foliage probably stay too small to be reliable ground cover over large areas, but make nice edging, or can cascade nicely from raised planters or urns.