Having done a bit of research, your USDA Zone is 10a, which means this plant should survive very well outdoors, as you've discovered. It's also chosen the best spot - light shade, because it burns in hot sun. It is useful for ground cover in shade situations, and is reasonably drought resistant, but will suffer from extended drought. It's a good plant to use, particularly in walls or raised areas where its 'babies' and leaves trail attractively, but is considered quite aggressive, in that it spreads easily. It is not, though, difficult to dig up and remove.
Regarding depletion of soil, they don't absorb any more nutrients than any other plant would.
To sum up, if it's not checked by unusual cold, waterlogging at the roots or extended drought, you may need to dig out parts periodically to keep it where you want it.