If there is a such a massive black hole at the center then wouldn't it suck in any light traveling above it, or is the amount of light put out by stars near the center so great that the light is sucked in slower than its produced?
A supermassive black hole (SMBH) is the largest type of black hole, having a mass between hundreds of thousands to billions of solar masses. They are belived to be located in the centre of almost all currently known massive galaxies. In the case of the Milky Way, the SMBH corresponds with the location of Sagittarius A*.
Actually, it may well be that the opposite effect to your idea occurs, as matter falling towards a black hole can also be seen emitting bright light and if the speed of this falling matter can be measured, it is possible to estimate the size of the black hole.
Space Telescope Institute
Disk around a Black Hole in Galaxy NGC 7052 (Hubble WFPC2 View)
If we can see the matter around the black hole, then by definition, it is emitting light as it accelerates towards the black hole.