Yes, the chuck will hold it, no problem.
Your description of the process is interesting. The picture seems to show that the lamp base is hollowed out. I'd have to question the wisdom of that. After all, this is a base for a lamp, and I would want some weight in that to counteract any toppling forces. As such, I'd have left it at the hole made by the forstner bit.
Most wood turners will not use an engineering chuck because in order to get any decent grip you have to tighten it to such a degree that it leaves marks (which are then nigh on impossible to get rid off). Typically a piece like this would have the centre hole drilled first, then be mounted on a jam chuck (matching the hole diameter) and held by the tailstock while the outside is shaped. Since this method of mounting pretty much guarantees a flat mount, you's want to start out with wood that has been planed flat and to size on both sides.
Hope this makes sense to you.
