Uh...no. Why do black holes suck everything in? Answer: They have mass, and lots of it. In order for the mass of the galaxy to diminish, that mass would have to leave the galaxy. Falling into the black hole at the center of the galaxy just moves the mass a little, but would leave the mass the same.
Really? Have you ever considered that the reason they 'suck' things in is that black holes (if they truly exist) have no 'mass' at all ?
If a 'black hole' is truly a 'hole' in the fabric of space, then it would not consist of mass, or it would not be a 'hole'.