Pinstar Plays Crab God [3]: Wallmaster 

I think so. They do have a hunger meter that slowly decays. While their attraction requirements depend on prey being present, meaning you'll never attract a predator with literally nothing for them to eat, a specific predator can get unlucky by having all nearby prey eaten before they can feed, leading to them starving to death. That said, just like with prey, the population will return to normal after a short delay. As prey get eaten, more will be attracted assuming the plant/coral situation permits them to. Luckily, many predators can nibble on invasive species so they not only help with DPS at night, but also refill their hunger bars on things that I want dead anyway.