In another thread in the Fish section, I mentioned how good Tiger Barbs are at ripping these worms from the substrate. So are Bettas.
Once they are in the substrate, you are stuck with them. Luckily, as has been said, their tails protrude into the water column to aid in breathing. That gives fish a chance to see them, but only the fastest, stealthiest fish will catch them before they pull back down below the surface. Cories and loaches can easily dig them out.
Like any creature, they will survive only if there is a enough to eat, so if you are not overfeeding, only a few will live -- and will not cause any harm to fish or plants.
What may surprise you, and what you should be more concerned with, are the "other" creatures that come with the blackworms, specifically those small, grayish oval-shaped flat worms that are present in every batch of blackworms I have bought.
I noticed a quarter-inch specimen perched on some driftwood after a feeding and ignored it, assuming he would be eaten. Well, months later, this quarter-inch gray worm had grown into a 5-inch pink worm and gave me quite a shock when I was uprooting some plants during a cleaning. I recall thinking, "hey, there's my khuli loach," and then remembered that I do not have a khulie loach

. This thing darted away and disappeared into a bunch of wisteria, where I could not find him. A few weeks later, I noticed "something" poking above the substrate and after a minute or so of poking and digging with a fork, I hauled this scary monstrosity out of the tank.
It was a good 5 inches long, yet could contract itself down to about an inch and a half. It was also very tough, as if made of leather, and resisted my attempts to cut it in half with the edge of the fork. I was prepared to rinse it down the sink drain when I noticed the salt shaker...

It reacted just as a slug would.