Yes the SS drive center can be 'driven' into the end grain for spindle turning, but, a little common sense goes a long way.
If the wood is hard or split prone, driving it on is almost guaranteed to split etc.
As mentioned drilling a small hole helps the center pin enter the wood.
Cutting two kerfs in the end provides a bite for the spurs without requiring forcing the center.
The purpose of the centering pin is to 'center'. Forcing it may enlarge the resultant hole and make that impossible.
The purpose of the spurs is to allow torque to be applied so the workpiece turns against cutting force resistance. They are not intended to be chisels.
