Are you talking about the inner race that always stays on the hub when you press the hub out? If so, no. You have to get that off just to replace the inner grease seal.
The puller I have was too big to get a grip so I used a dremel with a cut-off wheel and sliced a groove all the way across but not all the way through. Once you have a groove cut, use a propane torch and heat it up. It will snap and pop off.
If your talking about the spindle cup that receives the bearing, then no, that is part of the spindle.
Your hub should look like this before you have the new bearing pressed on.