Yes, this is the complete arbor to use with the Diamond Plus hole saws and is all you need.
The diamond hole portion of the bit is 11/4 " in diameter. Hope that is what you are looking for, when you asked for a thread size.
Your have to make a starter divot for the hole center first using just this bit without attaching the hole saw to the arbor. This makes it easy to see and drill the center point. Once you have the divot, attach the hole saw and used the divot to prevent skating across the tile. The spring action allows you to bring the hole saw down onto the tile surface immediately while staying centered on the divot. There is no need for the center bit to drill completely through the tile since the hole center is waste anyway.