I guess it would be possible, but it wouldn't be likely. Black holes are not cosmic vacuum cleaners. They don't suck everything around them in. The are just really massive objects. So while the center of most galaxies are believed to contain supermassive black holes, the stars in the galaxy are in stable orbits around the center and there is no reason to expect those orbits to decay in any reasonable amount of time.
Consider this similar question: is our Sun going to "eat" everything in the solar system? No. It won't.