diamond hole saws dont use a centre drill...thats why the guide template is a good idea. imo the existing hole wont make any dif..slow and water and you will be fine..........
You can make your own guide easy enough. Get a piece of PVC panel. Use the diamond hole saw to drill a hole in the PVC panel. tape the panel to the glass. Cut glass. You can either clean the melted/residue PVC off the hole saw before you start cutting or ignore it. Quick enough the saw and glass will "cut" all the debris off the bit and you will be cutting a hole in no time.